How do you know your team lead has talked to M?

I could be wrong, but from what you said, I would think there is high possibility that your team lead has not talked to M yet, because if she did, even M rejected, your team lead could come to you and tell you she has tried her best.

If I were you, I would ask team lead directly tomorrow if she has spoken to M yet, if she says no, then tell her why don't we go together to ask M? Put your team lead on spot and has no where to go but to do it.