なくてもいい

なくてもいい just says you can skip something. することはない goes further, telling someone not to worry at all (心配しんぱいすることはない).

てもいい permits doing something. なくてもいい permits not doing it, the opposite side.

なくてもいい grants permission to skip the act. ずに済すむ instead reports that it never became necessary, usually in the past.

なくてもいい denies the obligation ("you don't have to"). ないといけない states it instead ("you must").

なければならない means you must do it. なくてもいい means you don't have to.

なくて alone links a reason or a "but" ("not doing, so…"). Adding もいい turns it into permission not to act.

なくてもいい means you can skip it if you want (行いかなくてもいい). までもない means it was never worth doing at all (言いうまでもない).

なくてもいい releases you from the act (行いかなくてもいい, you needn't go). なくもない half-commits you to it instead (行いかなくもない, I might well go after all).