Possibly. Lavender does not take as kindly to pruning back into the old wood as the other plants you mentioned. You can only cross your fingers and hope.

In the future for your spring perennial, woody herb cleanup:

1.) wait until your woody plants start to waken for the spring - they push buds, start to get green again, whatever. Depends upon the plant.

2.) Trim out dead wood. It is always surprising how much is lost to just this. Sometimes enough vanishes here that you know that you had best leave the plant alone completely and let it rebound from the winter die-off.

3.) You can perhaps do some very light pruning for shape or vigor making sure to leave healthy buds and growing plant though many herbs like lavender need little to no pruning other than some dead-heading and perhaps a minor neaten. During the growing season, you never want to remove more than 1/3 of the living plant material. Keep this in mind for spring pruning too.

While you can hope, I think the new owners will be replacing the lavender.

FataMorgana