If it's outside, don't bother to prune it in winter, just clean it up in spring once the new growth starts coming out.

If it's inside, cutting it back a bit now will help it cope with lower light conditions, but don't cut into old, woody growth now; the plant doesn't have the energy reserves to heal easily after a heavy pruning. Lavenders get woody with age, it has nothing to do with how you prune it.

If it has one single growing clump it's not big enough to divide; once it has more than one rooting point, you can divide it then.

Enjoy!

Jim