I always wonder: how do Felids survive past the lair? Not that I've gotten that far with one.
I've played a couple modestly good Felid games[Haven't gotten any runes though, usually dying in the Lair branch rune-vault] and I can say that there are a few major ways:
1: Stealth/Hexes. Felids are stealthy, quick and have good aptitudes for both of these. Especially if you worship Dith, you can easily stab your way through Lair and farther.
2: Summoning. Felids have a decent Summonings aptitude. Summon Ice Beast alone carries them through Lair pretty easily. Past that, it gets trickier, but I've had decent success with Felids using Summoning.
3: Zerking. Felid berserkers are [un]surprisingly robust. Against a hydra or something, you pray to the RNG your Dodging doesn't fail you and go ham. You could probably get past Lair fine, although I'm not sure how much further you'd go.
4: Evocations. Nemelex or maybe this new one, Pakellas, both give Felids pretty good firepower/utility. Plus this doesn't require as much investment and is usually comboed with one of the above.
5: Transmutations. I've never personally gotten a Felid Transmuter off the ground, but Transmutations could do a lot to make up for a Felid's innate weaknesses. The Lair and Mines would probably actually be the hardest part for a FeTm, honestly. You'd probably have to make heavy use of Sticks to Snakes to swarm dangerous enemies, since Blade Pawsing and going full ham is usually fatal. After that though, you'll most likely have access to at least some of the higher-level Transmutations[Statue/Dragon Form]. And Spider Form & high speed will suffice for earlier in the Dungeon.