tbh I don't think it's really necessary for Ash to battle Lance, since he's basically overshot him anyway (in the lamest way possible). Also, him catching Mewtwo is hardly necessary, and I really don't think Mewtwo wants to be captured either.
Still, I agree with you on there being a lot of unfinished business left over for Pokémon, and no ending will truly feel 'complete' unless Ash ties up a few loose ends.
Glad to see you agree with me, even partially.
About Mewtwo, I guess to be a "Pokemon Master", catching the strongest Pokemon ever would be a big step to that goal. And sure, Mewtwo is not a Pokemon that wish to be captured, but Ash is essentially the best human he has ever bonded to in his life. If Ash captures Mewtwo, I believe their relationship would be like Goh and Suicune. I mean, Mewtwo would accept Ash as his trainer and would help him when he needs him the most, but instead of waiting at Oak's Lab with nothing to do, he would continue his "mission" to go helping Pokemon wherever they suffer.
Besides, considering the messes Ash gets trapped into, it wouldn't be hard for Mewtwo to face some Pokemon who might actually challenge his power. For example, Guzzlord might be a good challengoe for Mewtwo.