Frost killed mine the first year I put it in. Yours might survive.
Leave all the dead it will protect the remaining live growth.
Also cutting it off could promote new growth which could get frosted and die also.

You might think about goodwin creek lavender. It tolerates the frost and cold better. The latest cold snap killed the flowers but the rest of both plants are fine. It did get down to 27 here.

I think your lavender will be fine. Wait until you see new growth before cutting back. Answering your post would be easier if you included your location or Sunset zone. Al

I thought my zone was in my profile but I guess not - Palo Alto, CA (SF peninsula) sunset zone 15-16.

We have never had frost especially as these gardens are close to the stucco house, facing southwest - the walls keep the gardens warmer at night. This is a first!

This is a frosty December, but not near as cold as December 1990. You lavender will be fine. Al