But he did not have to do that in such a clandestine, private manner. Using "admit" in the question title is a bit leading. He — among many others, it was absolutely no secret — wrote to that effect publicly from at least 1979 onwards.
Der angestrebte 'Mokkatasseneffekt', das war der Wunsch der währungsstarken Länder zur Verteilung der durch zwangsweise Übernahme von Reservewährungsfunktionen entstandenen Aufwertungslasten auf einen größeren Wirtschaftsraum, kommt hier dadurch zum Vorschein, daß bei Gelingen der Stabilitätspolitik die BR Deutschland von einer gefürchteten Geldmengenexpansion und übermäßigen Aufwertung verschont wird, während die bisher weniqer stabilitätsorientierten Staaten durch ihre relative Aufwertung inländische Preisvorteile erlangen, ohne möglicherweise ihren Export stark zu belasten.
Vgl. hierzu Lahnstein, M., Zum Europäischen Währungssystem, Zeitschrift für das gesamte Kreditwesen, Heft 1/1979, S. 20.
— Harmit Picht: "Die Ziele des Europäischen Währungssystems aus der Sicht der EG-Staaten", Speyerer Forschungsberichte 8, Oktober 1979. (PDF)
—translation— The desired 'mocca-cup effect', i.e. the desire of the countries with strong currencies to distribute the revaluation burdens resulting from the forced adoption of reserve currency functions over a larger economic area, is apparent here in that, if the stability policy is successful, the Federal Republic of Germany will be spared the dreaded expansion of the money supply and excessive revaluation, while the hitherto less stability-oriented countries will gain domestic price advantages through their relative revaluation perhaps without placing a heavy burden on their exports.
That Lahnstein told this as presented in the quote from the question over a glass of beer in a lengthy conversation to Healey is at least partially what Healy reports. He writes about this in his autobiography (quoted below). That is analysed in — Philip Stephens: "Politics and the Pound. The Conservatives’ Struggle with Sterling", Macmillan: London, 1996 p. 6. But the exact words spoken that night, and as used by Healey remain in the 'told allegedly realm' (as analysed by for example — Harold James: "Making a central bank without a state", in: Olivier Feiertag & Michel Margairaz (eds): "Les banques centrales à l'échelle du monde.
L’internationalisation des banques centrales des débuts du xxe siècle à nos jours", Presses de Sciences Po, Paris, 2015.
The original phrasing of what was said seems to be a bit lost in the way the question's quoting style goes. Most other occurrences read a wee bit different for the portion after the semicolon in "depreciate; since Germany". Which is not central to "competitive edge for Germany" anyway, but seems to hint at journalists leading to interpretative conflation of spoken material or imprecise quoting. After the semicolon comes what the writer took from Healey's conclusions and inferences (that he made in hindsight even) from that information.
The exact quote in context would be this:
Scarcely anyone else in authority was in favour. Ortoli, the European Commissioner concerned, was hostile, since he had lived through the ill-starred experiment of the 'European snake', a machinery for keeping the continental currencies closely aligned; France had twice been obliged to leave it in humiliation. The French central banker, Raymond Clappier, was opposed for similar reasons. The German central banker, Ottmar Emminger, thought it was dangerous nonsense. The only important supporters I came across in European financial circles were the Italian central banker, Paolo Baffi, and Manfred Lahnstein. Baffi thought that if Italy were given a little more latitude than the others, it might provide a means by which the lira could crawl downwards without too much drama. Manfred Lahnstein supported it on grounds of Germany's national interest. His argument was, as always, simple and powerful: the mechanism would require the weaker countries to intervene on the currency markets to keep the stronger currencies down, and vice versa; this meant that France and Italy would have to pay to keep the Deutschmark lower than it would have been in a free market, thus keeping Germany more competitive, and other countries less so. That is exactly how it has worked – and disastrously so at times like the late eighties. When the dollar fell in 1987, making the United States more competitive, its trade deficit with Europe also began to fall. But it fell not, as was hoped, at the expense of the surplus country, Germany, but at the expense of other deficit countries, including Britain. The reason, as Lahnstein had predicted, was that the EMS had prevented the markets from pushing the Deutschmark up, once Germany had absorbed the reluctant three per cent revaluation forced on it in January 1987.
In Britain Edmund Dell was strongly against the EMS in principle from the beginning, as was the Treasury, while Harold Lever was strongly in favour. The Bank of England was mildly in favour, since they thought it would exert a useful discipline on British governments. The Foreign Office was strongly in favour; it is in favour of anything which includes the word 'European'. I was fairly agnostic until I realised, from long discussions with Lahnstein and others, how it was likely to work in practice; then I turned against it.
— Denis Healey: "The time of my life", Michael Joseph, 1989 (p438–9, on archive.org)
That the entire quote in question is not overly concerned with absolute accuracy is further amplified by linking the conversation Lahnstein had with Healey to Lahnstein being "then-German Finance Minister". He was that only in 1982, while Healey depicts in his book a scene from " during my last year as Chancellor", which together with the introduction of the EMS was in 1979. At that time Lahnstein was state secretary.
We see the inherent effect and how it was sold: Germany wanted to lessen the effect other countries could achieve by devaluing their currencies and presented that as a win-win situation.
Whether it really was in effect or really was planned to have that effect is another question.
For an analysis from a British perspective that looks specifically into the competitiveness factor for the German currency and economy, cf. — Edmund Dell: "Britain and the Origins of the European Monetary System", Contemporary European History, 3, 1994, pp 1–60. — Michael Spirtas: "Lukewarm Pint. British Policy Toward European Monetary Cooperation 1978-1992", Political Science Columbia University, May 1997 (PDF). If you prefer to read the German view of things, especially in relation to French policy and ambitions: — Alexander Spielau: "Die Politische Ökonomie von Wechselkursanpassungen. Auf- und Abwertungen in Deutschland und Frankreich", Dissertation, International Max Planck Research School on the Social and Political Constitution of the Economy, Cologne, 2018 (PDF).
Towards the commentary that this policy was a renewed attempt of continental dominance, this time not with military but monetary means: while a bit polemic, that's true as well, if you want to identify such a long game in economic and foreign policy.
Albeit not so much just 'to squash European competition', or "economic primacy", and not so much so against other European countries. The primary 'enemy' at the time of conception was the USA. And that was 'this time' a shared opponent for Germany, France, and the UK (plus smaller nations equally dissastisfied with American economic policy and dominance).
Roy Jenkins’ direct involvement with the process of Economic and Monetary Union (EMU) in Europe was remarkably short, lasting little more than eighteen months. Indeed, the period when he was, arguably, the key figure in kick-starting the revival of interest in the issue that would culminate in the launch of the European Monetary System (EMS) in 1979 was shorter still. It lasted only the seven months from his own decision in July 1977 that EMU should be the Commission’s number one goal, to German Chancellor Helmut Schmidt’s surprise revelation in February 1978 that he intended to make the issue his own priority. […]
The second idea, namely that Germany could be tempted to act, is harder to back up in the archival record. Certainly neither of Jenkins’ two bilateral conversations with Schmidt in the first half of 1977, nor that with Hans Apel, the German minister of finance, provided much indication of the Federal Republic’s openness to a relaunch of monetary integration. But the archival record does demonstrate that Jenkins had taken note of the Franco-German statement of February 1977 when Giscard and Schmidt had reaffirmed their belief in the desirability of progress towards EMU, since he specifically raised the subject with Barre.
Furthermore the whole text of the Bonn speech delivered in December was evidently designed to appeal to a German audience, with multiple allusions to both the amount that the Federal Republic’s own experience and approach to economic governance could contribute to any European debate about EMU, and to the way in which an export-orientated large economy like Germany could benefit from tighter monetary union. Jenkins was also very aware of Schmidt’s profound dissatisfaction with the manner in which Carter was steering US macro-economic policy. The Bonn speech thus went rather further than Jenkins’ previous statements about monetary union in highlighting the extent to which greater European monetary integration would lessen the global dominance of the US dollar and allow Europe to play ‘a major and perhaps decisive role in the restoration of order to the international monetary system’. And finally it is clear from the East Hendred record, that Jenkins originally envisaged this Bonn speech as the launch pad for his monetary ideas, again highlighting the centrality of Germany in his thinking.
— N. Piers Ludlow: "Roy Jenkins: Top-Level Politics", in: Kenneth Dyson & Ivo Maes (eds): "Architects of the Euro. Intellectuals in the Making of European Monetary Union", Oxford University Press: Oxford, New York, 2016.