I actually kinda like using Hitmonlee in RBY. Don't get me wrong, it's terrible, but when I feel like being weird it's a lot of fun. Finding a niche for Hitmonlee isn't that hard: Three of the Big 4 in RBY take extraordinary damage from Hi Jump Kick even unboosted, and Hitmonlee has access to Meditate. His role is as a secondary surprise sweeper (you shouldn't drop Tauros for it) best kept as a surprise late-game reveal when most of your opposing team is paralyzed - the nice thing is you can go nuts with your Tauros a bit earlier in the match to try to spread good chip damage around, and the element of surprise with using Hitmonlee at all can work to your advantage as your opponent may unwittingly sacrifice its hardest counters (like Eggy) earlier on. The set I'd use is
Hi Jump Kick
Hi Jump Kick is duh, and Meditate is necessary if you actually want a fighting (heh) chance to attack more than one opponent because if you don't OHKO and instead give your opponent a chance to hit back, Hitmonlee gets straight destroyed. One Meditate guarantees the OHKO on Chansey, gives you a good chance to OHKO Tauros, and does up to 90 to Snorlax. Hitmonlee's big problems are that he isn't as fast as you'd think he should be, he can't take hits, and he's walled by way too many things. So for this to work at all, most of your opponent's team needs to be paralyzed and the dangerous psychics (Starmie, Alakazam, and Eggy) need to be gone. It's not too hard to sleep Alakazam or Starmie (as they're usually leads) and it's also not too hard to bait an opposing Eggy into Explosion (or trade your own Eggy to take it out). If you bring Hitmonlee into a sleeping or frozen opponent to set up a Meditate, or get a Meditate off by forcing a switch, you can do some serious late-game sweepage. If the conditions are right (mainly paralysis and a bit of chip damage spread around), Hitmonlee is threatening to a lot of OU staples - the aforementioned Snorlax, Tauros, and Chansey, but also Lapras, Cloyster, Golem/Rhydon, even Jynx. That's practically half of the tier and again, three of those Pokemon you're virtually guaranteed to face.
Seismic Toss is to try to cheese anything else you'll face - Gengar, Exeggutor, Starmie, Alakazam, etc, and the last is preference.
Hyper Beam is stronger but only relevantly so if you get a Meditate off. Body Slam can paralyze.
For support, you should use a sleep lead to try to disable Alakazam/Starmie out the gate, and from there you need to be able to get rid of Eggy and spread paralysis, and get Tauros paralyzed and chipped and/or gone. So really, you'd probably just use it as your standard 6th slot filler with Jynx lead for sleep and the Big 4.
Fighting-type attacks have really nice coverage in OU, it's a damn shame they're just not on anything viable.
ETA: inb4 someone suggest a Counter set. I've seen people use Counter on Hitmonlee, and ... meh. A bunch of stuff gets Counter. That's not really a niche.