When I had lavender I never cut it down so I couldn't say if it will send out new growth from the roots. Mine didn't send out many new roots but sent out growth from the old branches. The only thing I can suggest is water it and wait and see.

I cut mine back every year to about 2". It sends out new growth quickly. How far back did you cut it - right to the ground or did you leave a bit of stem? It starts sending out new foliage all along the stems but if there is even an inch of stem left it will come back.

I forgot to mention, if you still have the cuttings and are concerned about the one you trimmed, make a fresh cut in the cutting and then stick it in water. It will root.

I need to cut mine almost to the ground every spring because there is always so much woody stem, then it always comes back beautiful for the rest of the season.

I do cut my lavenders to 2-3 inches in the spring. I do however wait til the dangers of freezing is over before doing this because I have killed off lavenders before when I cut it down too soon. hardpruning too soon exposes it's core to the elements and therefore can kill them off. if yours hasn't bounced back by now, it's probably dead. This year has been rather hard with our unpredictable weather. I've lost a couple of plants despite careful pruning. I think the frost killed off the roots of the plant. Anyway I still have plenty of lavenders and so much so that they reseed and I've little lavenders everywhere.

Ianna