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.
You can force her to level on console easily (and PC as well without any console commands).
Dismiss her (do this near the door of a building or dungeon so she will exit to go home).
Make sure she travels thru a doorway on her way home (this resets her so she can level when you re-hire her).
Re-hire her (this is when she levels to YOUR level).
Bing! she is now your level. The Dismiss / Enable just performs the same things that any companion travling thru a cell to cell transition does (in terms of resetting them).
Her inablity to carry much with decent heavy armor is a problem.