So I'm doing the quest for the MQ where I've got to go whack the Lich underneath Sentinel, but I just can't kill the guy.

This is pretty understandable. I'm only level 8, and my character is a secret agent kind of guy (Primary skills are Short Blade, Stealth, and Etiquette). Not exactly a Lich-killer.

I know I could just come back when I'm a higher level, but I'm wondering if there are any better options. Any artifacts or potions I might be able to hunt down that could turn the tide against a Lich.

This actually feels really cool, by the way - my character ran out of there with his tail between his legs and is now looking for something to give him an edge so he can go back and finish the job. I never got moments like this in Morrowind or Oblivion.

Spell Reflection would probably work. An enchanted item would be best, but you would have to be 5th rank in the mages guild to get that. There are spells, such as Shalidor's Mirror, if your character could buy and cast them.
No potions that I know of, and any useful artifacts are (probably) out of reach of a level 8 character.

This will sound stupid at first, but it can also work. Liches don't have an insane amount of hitpoints, and all their spells are area effect. If you can sneak up on them or rush them fast enough to hit them, they can finish themselves off with their own spells if you can resist one or two and live through the rest.

But really, Shalidor's mirror is a much better bet.

Or if you have a bow and some distance you can try to run down his mana pool.

I was going to suggest what Shades said. I once found an ancient lich at level 4 and as I was backing up, it casted a spell that lowered my health to near zero and killed itself.

Yeah, Shalidor's Mirror seems like a good bet but I haven't got any Thaumaturgy skills.

I am finding the occasional potion of magic or element resistance amongst the Thieves' Guild loot, but not a lot.

It's becoming more of a concern because I feel as though every part of the MQ now is jam-packed with Ancient Liches or, even worse, Ancient Vampires. How are you supposed to bring those things down?

A combination of high agility with decent short blade and dodging makes most physical combat something I can handle, but magic is just something I don't know how to overcome in this game.

I can tell you I killed two gargoyles, a vampire and a vampire ancient all at once at level 8. I had an enchanted totem with a fire spell and I pretty much stood in a corner and casted it over and over until they were all dead.

Most of these things can't hurt you unless they're close enough to touch you. That's what makes the lich so much worse.

I'm also at he part where I'm about to go to sentinel to fight the lich. I plan on visiting every mages guild on the way and seeing what magic items they have for sale. I was also considering potions.