I'm fire and if I get a lot of HS and fewer clearcasting states, I can have some serious mana problems myself. I do keep a rank 1 frostbolt on my bar in case a valk is out of range of the melee stunners (and for beasts on saurfang sometimes), and if I'm nearby, I definitely do a quick CoC, but I'm mostly able to leave the stunning/slowing up to melee for the most part. Anyway, a lot of times I find myself needing to evocate, usually after the first transition phase. I just pile up with the group before the valks, wait till I get a HS and do a quick hasted evocate. That seems to help me a lot. I sometimes end up doing it again later on (ended up completely oom on our last kill and had to evocate at the beginning of bloodlust UG). But fire really does shine on the LK fight. Phase 3 vile spirits w/ lower health helps the healers a lot, but I do pretty good dps on all the phases.
Good luck on your LK kill. I've found that it's one of those fights that's a dance that, once you do it right becomes SO much easier each kill afterwards. Don't forget to nerdrage when everyone dies at 10% about noobs wiping the raid! lol