Litch: apart from generally low level items which are certainly gimping your threat output (doubly so for the weapon slot, which would be by far the largest jump should you upgrade it), the set you're wearing on armory is extremely stamina oriented. While it certainly has its place on a hard hitting boss with rogues and hunters giving you bonus threat, in most other circumstances it's really overkill - at the expense of threat generation and avoidance. You may want to consider swapping (quite) a few DPS-oriented pieces in, every time your survival doesn't feel threatened.

Additionally to Argatha's proposal, in heavy AE situations I'm constantly tabbing (and Shift-Tabbing) through all enemies, watching Threatmeter to find targets where I am low on threat and/or dd's coming close, so I can get some more threat on those targets via Maul and maybe Mangle. If you identify 2 targets where you need more threat, check if there's a melee second on the aggro list and hit that mob first.

Best solution for threat problems with big groups is using nameplates with visible threat. (Aloft is good mod to get beater visual effects)
When you got some mob that is near to lost threat on him glow of nameplate will change, you will have couple of second to reaction (taunt or simply dmg him more).
Additional benefit will be that you see what mobs are tanking by you (some can by tanks by other tanks) and you can focus only on your targets.

BTW some times is good to use Berserker on trash, free boost of threat on demand.

Due to the way our raid days work (we don't raid on Weds) and some attendance issues, we're starting our first serious LK attempts tonight after a couple of short tries at P1.

How do others at this stage feel about HP levels for tanking the LK? It's probably going to be my job and at present nothing has really required that I optimize in a particular direction, therefore I am using a mix of 30sta, 10agi/15sta and 20agi or 10agi/10hit gems (see my armory)

This leaves me around the 54-55k mark depending on trinkets and I'm thinking this isn't really going to cut it. Do you think it's worth me quickly going for 30sta gems across the board to make things easier for the healers?

I think you will want to go full-on Stamina for this encounter. Our main LK tank is a DK, and there were plenty of times where his health pool was just a bit too low. LK can do some HUGE hits, so a very large HP pool (~65k or so) can be extremely helpful. If I were tanking this encounter I'd go all Stam

Hit and Expertise both work out to be pretty similar in tanking situations (I'm assuming you're talking tanking based on your armory); both stats are mainly there for threat generation, as the "parry-haste" mechanic that wrecked so much havoc in BC is largely missing from most WotLK bosses. I personally like to have a decent amount of hit so that my Growls don't miss as often (though when I simply can't afford to miss a taunt I use Glyph of Growl in place of Maul), but Expertise is just money for threat. A balance is nice, and there are no specific "soft/hard cap" numbers to really shoot for as a tank, but rather you get enough so that your threat is where you need it to be.

I've never been worried about being below hit cap for a long time. It depends on the fight really. Fights like Heroic: Deathwhisper you really don't want to be missing anything so I was drafting in some DPS gear to reach hit capped and some DPS trinkets to max threat. Most fights though you'll get the Tricks/MD's though so threat isn't much of an issue.

This is a fight you purely want to go for stam given the mechanics. When off tanking there is no incoming damage that is really a threat, with the exception of multiple shambling horrors enraging at the same time and hunters being slow on tranq (but that is what barkskin is for).

The main threat is Soul Reaper which hits for ~40K upfront, another ~40K in 5 seconds and gives the Lich King a brief +100% damage buff once it goes off. Once spirits are down you and the other tank should be swapping for this and using a cooldown if you are the one taking the increased Lich King damage. However even with Barkskin up I would take hits well over 30K and up to 40K, at which point you need a health pool that can take 2 of those with only some hots/earthshield/shield giving some cushion rather than hoping you avoid or a holy light and another heal hit you before the next swing.

Just a note its 100% increased haste not 100% damage (I think 100% damage would probably be one shotting our warrior tank). One of the easier ways to mitigate this is to ranged taunt the Lich King and then when he gets to the far tank have the MT ranged taunt back. You negate almost the entire 5 second window that way which is much safer then eating the 27-30k dps the lich king starts outputting when he has that buff.

Does the first 20% reduction from barkskin diminish the 12% reduced by 4P enrage? or is it just a flat 32% reduction?
As well as the other way around.

Since it's percentage based, it stacks additive. Flat 32% if you pop both.

Do you have any evidence for this? Alot of other mechanics that use percentage-modifiers stack multiplicatively, so it's not at all obvious that 4T10-Enrage stacks additively with Barkskin.