Sylvester Archipelago

She has some kind of special ability that allows her to heal during battle?

Second Healer.

Added after 59 seconds

But is it possible at all?

It is possible, but all memories related to activities within the order will be erased.

Added after 5 minutes
As dawn approached, the mercenaries reached the camp. A skirmish with a wild beast had slightly worn them out. In addition, Lucina felt unwell due to catching southern fever. Kaeldrima was bitten by a poisonous snake on the way to the camp.

Lucina uses the Southern Fever Remedy borrowed from Kaeldrima.
Kaeldrima uses Universal Antidote.