Yeah, the way not-very-scientific books and films tend to present time travel, except for mutations, M and LM are the same person with the same DNA.
Except for the “but both lived in different dimensions and conditions and are complete opposite of each other” statement which I don’t understand. What “conditions”? How are they “complete opposite” – in what way?
I can imagine that the multiverse effects of time travel could play a role, but that’s all science fantasy and I’d have to invent the details.
Also, the butterfly effect of “altering the past”, or just simply being in a different timeline or multiverse, could mean that M never even gets born in the second timeline/multiverse.
In fact, I would tend to think that all bets are off when you time travel, in two ways:
1) If traveling into the “past” creates a new multiverse/timeline, I wouldn’t consider there would be any guarantee that it would be identical to the past of your origin multiverse/timeline. So all bets would be off.
2) As long as events are not super-pre-determined/doomed to unfold in exactly the same way, even in you arrive in an identical past, the outcome of all future actions and reactions would be different, and could unfold in very different ways, so M may be unlikely to be born, and even if a child LM is conceived by the same parents, there is no reason to assume that the same sperm and egg would be involved, nor that they would bond and mutate into the same DNA sequence that M had. So LM would be a sister at best, not a clone.
And… since every other action and re-action would be happening anew, the whole world would be different, and that many years into the future, probably LM would not even be conceived by the same people except by an unlikely coincidence, history would be different, the people would be different, etc.