Who says he needs X for his mantle, it is his by birthright and he would grow into it anyway, just he has been set up in game to die if he gets no access to X at that moment and it might have well taken him way longer to grow into the power he wields now already without having X as a focus for his power and the power saved up in the Lake to help him. The power/mantle of Winter King is his though or chose him for a reason and in the end not based on any artifact or lake created by Merlin, they are just crutches in the end.
I am also pretty sure MC is not even close to using his true and/or full mantle/potential at this moment in time. He is still a broken mongrel (as Akane's pet likes to remind him) and Emily, his chosen, the Lake and X are just stop gaps for that in the end and he will have to grow quite a bit still before being able to wear the full mantle of the Winter King or his father's (as I suspect might be his happy end if will be able to change those two mantles) later if that is his future destiny with Emily by his side, nor is he likely without those crutches the strongest around yet and possibly not even with yet. I would not be surprised if both the Horned God and Odin or other firstborn could destroy him at this time if they wanted to, just they need what he could become.
It is true that in this reality at least (that the game mainly or solely plays in) the MC should never live beyond that moment without Emily and X as setup by the Voices and Merlin (though we do not know or will likely ever know if he would have lived anyway despite that setup and somehow would have survived through his own power or actions of his Mantle wanting to keep him alive and there if he had chosen against the path Merlin and the Voices had chosen for him) and would never assume his mantle since he would have almost certainly died. So yes, he needs Emily by his side as far as we have been told in game to live long enough to ever be able to grow into his power if the plans of the Voices and Merlin works (fact they needed a safety or two though shows they are not infallible in themselves or were sure how it would turn out, like the bomb thingy with the lake if he somehow survived anyway
). It is still his power and mantle though and destiny, just as Emily has her own destiny and fate which might well be very different if MC was not by her side.
That may not be true for all possible realities though
and who knows possibly MC is at end of Act 2 visiting a reality where the Goddess never left for example and MC would not have needed Emily since he is not a mongrel, just bring someone back that the Dev let slip in past he liked a lot ) or gets to see what happens in a reality of a Winter King emerging and taking up his mantle without Emily by his side or he gets an option in that reality to mend his lack or learns something else important or all or none of the above, only Droid knows what he intended with that until he reveals it.
