As I love etymology and current usages and how they interplay in various subcultures, attempting to discern lemma from proposition from theorem has been interesting and I’ve learned much in a short time.
It seems that your usage of lemma is proper in every which way. As long as it’s used contextually (“let’s suppose this is valid but only for this particular situation and not generalized as a universal. If we accept this as contextually valid, then…”), it’s a lemma.
But if the lemma is “lifted out” of its context and attempts are made to make it a universal, then it rises to the level of proposition.
At least that’s my general impression of them from a quick synonym search, my own very generalist knowledge, and no experience in actually *using* them at all in any way for anything.
I just like understanding the ‘gist’ of concepts enough to be able to answer if someone says, “Hey, Ken, what’s a lemma in mathematics?” I could then give a couple of sentences that get them in the ballpark of ‘close enough’ for their needs in that situation.