As was pointed out on that other question you linked, this is a surprisingly tricky sentence!
Let's slowly build it up.
It will take someone else.
What is "it"? Stopping Voldemort again. Implied but never directly said. As for "take", we could say "need" instead, just to be slightly clearer.
[Stopping Voldemort again] will [need] someone else.
This isn't "someone else" as in "we need a different person", but as in "we need other people prepared to do what you did, Harry". When will they be needed? "Next time" (that is, the next time that Voldemort tries to return).
[Stopping Voldemort again] will [need] someone else who is prepared to [do the same as Harry] next time.
Now, Dumbledore is saying that this someone else doesn't have to do much. Hence, it will "merely" (or "only") take someone else. This may sound like it's demeaning Harry's efforts, but it's meant to be reassuring Harry: standing up to Voldemort is not very difficult or unlikely after all, and it doesn't take someone extra-special to do it.
[Stopping Voldemort again] will merely [need] someone else who is prepared to [do the same as Harry] next time.
What, exactly, did Harry do that Dumbledore says they need other people to do (or be prepared to do)? "Fight a losing battle"--or what seems like a losing battle. (Dumbledore omits the word "like", but I'll leave it in for this one example.)
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight a losing battle next time.
[Stopping Voldemort again] will merely [need] someone else who is prepared to fight what seems [like] a losing battle next time.
And now we just replace the bracketed bits with the different wording Dumbledore uses, and we have the sentence (okay, part of a sentence) that you bolded.
It will merely take someone else who is prepared to fight what seems a losing battle next time.
Best Answer
It refers to the to worry or pray. One refers to worry and the other to pray.
What he means with that is that if you do not have worries, you do not need to pray. He refuses to worry, which means that he does not have any worries and that he has no need for prayers.