In 1869, before Lenin was even born, in The Crown of a Life it was written by Isa Blagden:
If a lie is only printed often enough, it becomes a quasi-truth, and if such a truth is repeated often enough, it becomes an article of belief, a dogma, and men will die for it.
I only see recent (last 15 years) references attributing it to Vladimir Lenin.
I think the misattribution grew out of a statement like this one in the 1966 book Great China Danger:
Actually, Peking has operated, as Moscow has since the days of Lenin, on a number of principles which taken together can be called the technique of the "great lie." Among these are: 1) make it big enough and people will believe part of it; (2) repeat it often enough and you will convince some people; (3) say it in enough different ways, and you will convince others...
So it went from saying that is what Lenin did, to making it be a direct quote.
Also, a different Lenin is quoted in the 2001 book The Duke of Havana: Baseball, Cuba, and the Search for the American Dream:
“There's a saying in Cuba: A lie repeated many times becomes the truth,” said Lenin Rivero
The misattribution could have also originated from this quote. Lenin Rivero is a Cuban who defected to the USA in 1998 and who was named after Vladimir Lenin.