I've seen the quote:
"One quick way to destroy a society is through its music." Vladimir Lenin
on (Russian?) Facebook:
and is also mentioned in the book The Authentic Musician (John Haddix, 2011):
The source referenced there is The Marxist minstrels, a handbook on communist subversion of music (David A. Noebel, 1974),which appears to be the source for this supposed quote. This book is reviewed here, basically stating that the author is a crackpot (more or less the same conclusion is reached here). I can not access this book.
The quote is not present in Wikiquote so I'm very much inclined to discard this as an outright lie, but it'd be nice to see where this person got this from the book itself.