You could also take this as the demeanor of the Warlord and the respect he engenders having an influence on the character:
As your consciousness fades and you feel your life ebbing away, you think of <the Warlord>, that noble warrior and tactical genius that has seen you through so many conflicts in the past. You think about how you might be letting him down if you were to die right here in this moment, still so far from your party's goals. Hanging from a final thread of conscious thought you realize that you cannot allow yourself to fall here, no matter how much you might hurt, because you cannot bring yourself to disappoint <the warlord>.
More of an inspiring presence, really, but other than flavor text there's nothing to say that the healing word has to actually be words.