If you are a PS3 player or Xbox player the best thing you can do is honour her death, with Thalmor blood.
My Lydia was burnt to death by the Thalmor so I used a dragonshout to bring down the perpetrator.
I took a blade forged from Eorlund Gray-Mane of Whiterun, I screamed Lydia’s name as I beheaded the Thalmor Warrior that snatched her life.
I was going to make an honest women of her ( I later found out I can’t marry her anyway).
You can get other housecarls by becoming Thanes in other major cities; do a quick Google search to find out which quest to do.
NOTE: If you are developing conjuration, mark where she died and bring her back to life when you have mastered Conjuration skill dead thrall, she will not be the Lydia you knew but she will fight like the Lydia you knew.