Lydia can be killed by the player. She will not die in a fight against an NPC but if you inadvertently strike her in combat or choose to attack her, she will die and can only be resurrected by returning to a previous save.
Yes, Lydia is one of the potential spouses.
Talk to her and ask to rearrange her equipment then add stuff to her inventory!
Lydia Lipkowska died in 1958.
Lydia Sigourney died in 1865.
Lydia Davydova died in 2011.
Lydia Boucher died in 1971.
Lydia Veicht died in 2007.
Lydia Wahlström died in 1954.
Lydia Mei died in 1965.
Lydia Pinkham died in 1883.
Lydia Gibson died in 1964.
None of your companions can die if they are following you, but they can die if they aren't. An example would be if you are in combat and you tell her to part ways and she gets killed by the person or creature attacking you because she stopped following you. I used "she" because I am referring to Lydia, your bodyguard you get from Whiterun for being the Thane.