Make sure you are getting enough salt (NaCl), but not too much. Lamotrigine is a sodium channel blocker and can lower the amount of available sodium—which is important for electrolyte balance and maintaining blood pressure—in your body.
I found I had terrible headaches in the first several weeks of starting and increasing lamotrigine and that dipping a wet fingertip in some sea salt, licking it off, and chasing with a small glass of water actually helped or made the headache go away completely.
I might be more sensitive to this because maintaining my electrolyte balance has been a longtime issue for me, way before my bipolar 2 diagnosis. But it’s something you could try.