Many couples break up due to a lack of communication. ( I’m not fan of / of so close to each other) Dropping an article is idiomatically common with ‘lack of’. However, I wouldn’t get into this habit. One place there will be no indefinite article is usually the beginning of the sentence. Lack of communication is one of the lead causes of break-ups.

Yep mate, sounds fine. You could say “because of their lack of communication”to make it sound better