Edit:
As pointed out in the comments, my initial thought on this contract is wrong - because you also remove the hero when you lose the Riddle-game.

Original post:
I don't know what to make of this contract. It seems to me that this is the choice for a no-contract-fits-my-deck. There is no real downside to it. Even if the player doesn't discard any cards for the Riddle Game, you have a good advantage (at least in the early, decisive turns) due to the relatively strong attachments with the Guarded keyword.

Since I've bought Mountain of Fire expansion I was trying to find a place for Éomer in one of my decks and failed each time. While his response sounded great, in fact most often he didn't work since he needed serious attack boost (and only in-sphere valid option is Gúthwinë) to really make difference and what is more important, he lacked targets. Apart from secrecy decks (which don't seem to be really best space for him) in most of my games I don't want to keep enemies in staging area - at least weaker enemies and against tough guys Éomer can't shine. He definitely has good interaction with Fastred, but I don't have him in my collection. I've always chosen his tactic version then as it is way easier to use.

That being said, I've recently started playing Ring-maker cykle again with freshly bought Dream-chaser cycle cards (yes, despite playing the game for ~10 years now I'm not rushing) and found him really strong. Beginning of Ring-Maker cycle is great for him since I've often some glass canon Dunlendings in staging area, great targets for Éomer armed with Spear of the Mark and/or Firefoot. Of course he needs access to tactics sphere, but he pairs up really well (not only thematically) with tactics Éowyn - her low starting threat means that I don't have to engage everyone and she covers his lack of willpower. But that wouldn't be enough to make him viable. To give him targets, I've used Fresh Tracks, but Terrible to Behold is also amazing choice since it can send back enemies that I engage automatically in specific scenarios. 2 copies of both events are fine to give him flexibility. But definitely the most crazy combo I've discovered recently involves Grappling Hook. I don't need anymore to have an enemy left in staging, I can wait for them to appear. What is more, while still I'm willing to boost Éomer with Firefoot and Spear of the Mark, with the Hook I can wait for staging and then add him contributing 6 points (!) to the quest and 7-strength attack (difference due to Spear wording, at least this is my intepretation) - enough to kill a lot of opponents. Yes, it needs 4 cards, but hey - Éomer just needs some deckbuilding around him, it's fine by me. Definitely more interesting option than Late Adventurer.

Very satisfying hero to play. When he is working, he is really outstanding.

I like this ally in Lothiriel+Elf-Friend decks, as Lothiriel shuffles her back into deck, which makes for a lot of recursion over the course of a game. You can also use her with Thranduil to get a different timing on your reshuffling, e.g. to get a combat action event back before chump blocking.

I'm a lumberjack, And I'm okay, I sleep all night, And I work all day!

(He's a lumberjack, And he's okay, He sleeps all night, And he works all day.)

I cut down trees, I eat my lunch, I use the lavatory. I hope there are things in the forest, so you don't have to pay for me.

(He cuts down trees, he eats his lunch. He uses the lavatory. We hope there are things in the forest, so he can play for free. He's a lumberjack, And he's okay, He sleeps all night, And he works all day.)

I'm a lumberjack, And I'm okay, I sleep all night, And I work all day!

(He's a lumberjack, And he's okay, He sleeps all night, And he works all day.)

I cut down trees, I skip and prance, I like to press wild flowers, I attach cards to the forest, to level up my powers!

(He cuts down trees, he'll skip and prance, he likes to press wild flowers...? He'll attach cards to the forest to level up his powers! He's a lumberjack, And he's okay, He sleeps all night, And he works all day.)