Hi and welcome. Sadly, not really, Lavenders do not like to be pruned back into brown wood. What you can do is to take some of the nice green shoots as cuttings and then replace the old bush with them.

And when you grow new lavender, remember to clip it over at least a couple of times of year, after the main flush of flowers is done, clipping off flowered stems and about an inch of foliage. This will extend the life of the plant by lengthening the time it has before it gets too woody. It's usual to replace them after about 5 years, once they do get woody.