After i finished Thalmor mission Lydia is gone and i cannot find her!
Does anyone know where she is?

Check the castle in Whiterun. She mite be there chilling in the feating hall or if you own the house in Whiterun then try your bedroom, she is normally sitting there endlessly eating bread for some reason.

If you made her wait some where and forgot where you left her, you might have to wait a few days until she returns to Whiterun.

Truth

Lydia is not at any places mentioned above!
How can i get a new companion?

did you check Delphine's chest maybe she put Lydia in there with your other stuff