The Healing Touch glyph and 5/5 Naturalist are your friends.

I've written about this recently but didn't really expand on it with respect to the Lich King fight. In an ideal world, a glyphed and specced Healing Touch wouldn't be the least bit necessary, but there's a lot of burst damage -- particularly on phase 3 -- that made me reconsider speccing back out of it. If you've gotten to the Lich King encounter, odds are pretty good that you're at the soft +haste cap (856) without having to spec into Celestial Focus, and that frees up a lot of talents points that allow you to spec into Naturalist without gimping yourself. It's really the loss of a major glyph slot that you'll feel more than anything else, so use your best judgment over whether you can afford that.

There are several situations where you'll need to be prepared for damage requiring quick healing even if you don't HT:

• Mopping up Infest damage in phase 2: The raid will be in constant motion in phase 2 between handling val'kyrs, stacking up for impending spawns, and dodging Defile. Infest will be hitting during all of this, obligating the heal team to top everyone off while running their collective ass off. While Chain Heal, Prayer of Healing, and Circle of Healing will wreck anything you can do during a fairly stationary phase 1, people will be all over the place in phase 2. I have to admit I prefer Nourish for this damage -- using HT a lot for Infest gobbles way too much mana -- but HT's a good way to spot-touch people in far-flung corners of the platform.
• Soul Reaper: Tanks losing huge chunks of health at periodic intervals is guaranteed.
• Getting a fast heal on a player who's been hit by a Vile Spirit: Theoretically no one should be getting hit by any of these -- and as your raid gains experience, the damage they cause will occur less frequently. But odds are good that someone (and particularly melee) will eventually get hit, and that's a 17-20K hit that you might have the pleasure of trying to heal on multiple targets.
• Getting a heal out quickly on the player targeted for Consuming Shadows: This is the big one. The target of Consuming Shadows takes a massive amount of shadow damage each second, and if you can't keep them up through 6 seconds of it, Arthas gains a damage buff that will wreck your tank unless you get a big cooldown on them stat. On 25-man, the second Consuming Shadows tick will usually kill a player, so your margin for error is very slim. Getting a lightning-fast 7-10K heal on the player in question is often a lifesaver, and/or a Swiftmend -- preferably both.

Don't panic if you get ported to Frostmourne.

In phase 3, Arthas gains the ability to Harvest Soul, which we've just discussed. I should probably add that, if you're the target, there's nothing you can do to avoid the damage. You can't pop Barkskin, and you can't heal yourself -- you are entirely at the mercy of your raid. Assuming you survive, you'll get ported inside Frostmourne and confront two NPCs -- Terenas Menethil, battling for his "life," and his captor the Spirit Warden. You need to DPS the Warden down before it kills Terenas, or keep healing Terenas (his damage increases as his health rises) and let him kill the Warden. This is made somewhat more complicated by the 8-second Soul Rip debuff that the Warden will attempt to channel twice while you're in Frostmourne.

I've seen some commentary online that the worst possible person to get Harvest Soul in phase 3 is a balance or restoration druid, because we can't dispel the debuff the Warden channels on Terenas (Soul Rip) and don't have easy access to stuns.

Bu-hu-hu-hu-huulllllllcookies. You're a druid -- act like one! We've got two stuns available through bear and cat form (and a third if you're a tauren with War Stomp), and there's no law saying you can't HoT Terenas up and jump into form to anticipate the channel. Please see handy-dandy instructional video above, wherein Allie got ported twice in a row and managed not to blow it.

If all else fails, just remind yourself in a very soothing tone of voice: "It could be worse. It could be heroic."

But I'm trying not to think about that part.