If you are on a console you are hosed unless they patch it so Lydia levels with you.
On a PC Lydia is a studdette if you do the following.
Tell her to leave and then hit ~
Click on her and type disable (she goes poof)
Close the console
Open it again and type enable.
Shes back.
Tell her to follow.
Shes now your level.
As for her dying, no she does NOT simply die because shes hit in normal combat. Every Lydia death I've had can be traced back to me, either a spell or a hit or a shout. I found out the hard way that using unrelenting force on a boss while Lydia was on her knees will kill her. I've seen her in a fire trap SLOWLY crawling out of it on her knees while surrounded by flame. I've seen her take arrows on her knees (dont' say it) from guys who could one shot my mage. EVERY one of my Lydia "oh crap she died" was my fault, though sometimes I didn't realize it at the time. You have to be careful with fireball, runes, etc. Even power attacks because she does like to jump in front of you and the rather odd 'range' of weapons means it easy to hit something that it doesn't look like you could hit on screen.
Thanks for the console commands, I'll try them.
If you say I'm doing it, OK... I know it was me with that Chain-Lightning staff... I hate fighting in groups, even groups of two. But there were a couple of times she died that, if it was me, my straight-line spell bounced to my rear (and I don't think that's possible), because she was nowhere in the line-of-fire. All I know is Lydia dies a lot, if I'm not careful of her. As a result, I watch for Lydia first, then the enemy I'm trying to kill, not a safe tactic if I want to survive.
What I wonder is why I take her anywhere, now that she can only carry a few potions and such. It's just that she gets so depressed when I leave her home.