What is funny about Frankie's line about aspiration?

Earlier, in the kitchen discussing "empathy", Johnny said, "You see, every day when I'm shaving, I look up a new word."

This is a reference back to that scene. The joke is that "Have you been shaving again?" was a substitute for "Are you using the word 'aspiration' / having 'aspirations' because you just looked it up in a dictionary?" and the implications of that. The remark was meant to be facetious.