I think I did this right but just in case I'd like to ask our forum experts:

Playing Rhosgobel I revealed "Exhaustion" from the encounter deck. Landroval already had 2 damage and was exhausted. Bilbo was also exhausted. Both got killed by the card effect, so I discarded the two of them. I thought for a while if it would have been possible to discard Bilbo and to use Landroval's reaction to get Bilbo back in play. I dismissed this idea though, as Landroval is already dead in the moment in which I want to use his reaction.

So, did I for once play it right, or did I punish myself again needlessly?

Yep, when something deals damage to multiple characters, all deaths occur at the same time, so Landy can't use his Response.