Yes, these purchases do allow you to use the title of "Laird" or "Lord". Please see the official government guidance on titles for passports (.pdf link), which states (p. 13/14):
Bought and styled titles
Bought titles may be sold by internet companies.
In the past, holders of bought or styled titles had to write to the Manorial Society of Great Britain for confirmation of the right to use and be known by a title. This society is a private company, in direct competition with many others that deal in the buying and selling of titles.
You must never tell a customer to contact the Manorial Society of Great Britain for confirmation, unless they have bought the title from the society.
You must only add an observation for customers with bought or styled titles, if it’s
included in this guidance (for example, a manorial title)
(My emphasis, some text omited). Which clearly states that the passport office will include a title such as these on your passport, what more official record could there be? But wait, what was the bit I omitted:
Styled titles mean self-styled or presumed titles that customers have created for
Huh. So you could just make up a title for yourself and use that? Yup, you don't actually need to buy the package to call yourself a Lord, you can just do it. This is unsurprising because in the UK, unlike in some countries, your name is simply what you call yourself and you are free to change it to almost anything on a whim: although something like a deed poll is useful to prove that you are going by the new name for formal purposes.
In fact, this applies to all titles in the UK. It even extends to titles like "Dr", unless you're using them to fraudulently misrepresent yourself or mislead the public, as in the famous case of Gilian McKeith.
Of course, calling yourself a Lord doesn't give you any privileges or authority, and you will get short shrift in high society if you tried to use such an internet title. Real and meaningful Lordships are tracked and validated by The Court of the Lord Lyon in Scotland which is also the body responsible for Coats of Arms in Scotland.