is the phrase you're looking for. does literally mean "become late", but this "late" is more along the lines of an event becoming delayed or postponed beyond the expected time. The context you're looking for is a person being late for a scheduled event, which is what conveys.
Either or can be used. The latter adds an undertone of regret.
works as an alternate for , if you want to avoid :
And depending on the speaker and situation, can be substituted for , which was covered in this question.