How to exclude a lapsed membership from mailings
I may have misunderstood but assuming you are using CiviMember an easy option is to make a Smart Group based on the membership criteria - and use that Smart Group as your Mailing List.

For example, go to Advanced Search, expand the membership section of the search, set the Membership status to eg New, Current and Grace. Then the lapsed members will automatically be excluded until they rejoin at which point they will be included in mailing.