My characters are level 13/14, I've cleared most of the Overworld and some dungeons and I've been working on the Arena. I've hit a bit of a wall with the Lich enemy. He hits my party with an instant-kill attack (it's not the damage as such that's killing them) and I can't survive more than two rounds.

I've tried Holy Word against the Lich but it doesn't finish him off fast enough to survive the fight. Do I just need to level more, or does anyone have strategies for fighting a Lich (and enemies with similar instant-kill abilities)?

Liches are among the few scary enemies in MM3. Since you'll be around lvl 90 at the end of the game it sounds like you should explore some more dungeons first.

But try the Implosion spell if you have it yet. I don't remember if liches have magic resistance. If they don't, an Implosion spell should insta kill a lich. If that doesn't work you'll definitely need higher level hard hitting characters to kill the liches ASAP.

Level 13/14 is quite low for fighting a lich.
Lichs do magic damage. Raising you magic resistance will reduce the damage taken. Raising the luck stat (you can raise it temporarily by throwing coins into the well in Baywatch) will improve the chance not to get instant-killed if damage is taken.

But exploring is more rewarding than fighting in the arena. If you haven't done it yet visit the Cavern below Blistering Heights next.

Power Shield protects you from damage equal to the casters level. A level 10 power shield absorbs 10 damage on each hit. Now here is the thing if the damage is 0 the attack is counted as missed and special effects are also canceled.

Implosion is an energy spell because of that it doesn't work that good against enemies with energy resistance.