So, let's say that I use Lore of Imladris to completely heal Wilyador just prior to defeating Rhosgobel's 2b quest card. That would bring in the 3b card and it's effect:

When Revealed: Heal 5 wounds from Wilyador for each Athelas objective card the players control.
If Wilyador is completely healed when this effect resolves, Wilyador survives and the players have won the game. Otherwise, the players have won the game.

What happens if, at this point, I control no Athelas cards? Wilyador would be fully healed, albeit not through Rhosgobel's effect. I see nothing that lists controlling one as a winning condition. The only condition is that Wilyador must be fully healed when the effect resolves. But doesn't the effect resolve regardless of how many Athelas I control? And the end result is that he is fully healed. Would this give me a win? It seems completely contradictory to the spirit of the quest. Sort of, "well we didn't find any Athelas, but the elves healed him anyway" kind of thing.

I'm probably going to house rule that you must control at least one Athelas, so as to remain within the spirit of the quest, but I find no particular rule to back this up. Is there something I'm missing?

You have to look at each sentence separately. Healing with the Althas is not manditory it is just an effect that happens. After healing, via Althas or other means beforehand to result in 0 wounds, if the bird is completely healed you win the game.

Using Lore of Imladris is fine, but keep in mind that that can heal a maximum of 5 wounds on Wilyador. But yeah, the 3rd quest card doesn't care how you heal Wilyador, just that he is healed.

Thank you both. I brought it up because it nearly happened on my first run through when I had two Lore of Imladris in my hand. Which, at that time, would have healed Wilyador completely. This is how it finally went on my third try:

Wilyador had 14 damage. Played Lore of Imladris, which reduced it to 9. Then, claimed my second Athelas, right before flipping the quest card and that completely healed him. I also had Glorfindel and Radagast ready with a combined 5 heal, which wasn't needed. I can see now, with a few games under my belt in this scenario, that the Athelas is far more indispensable than I originally thought because you may not always have enough healing on hand. So I will modify my strategy accordingly to increase my chances of getting them in multiples.