Yes, but into the old wood if its not too straggly.

Just remember that lavender doesn't sprout from bare wood. Not much of an issue with yours, Amsterdam, but something to consider with older plants.

Thank you Jimmytheone and Tugbrethil.

Sorry but I did miss out the 'not' into the old wood. But having said, I did cut mine back into the old wood and low and behold it has come back and is thriving.

But you don't have to wait for it to go right over and do it all at once. Keep dead-heading as soon as the heads start to brown and it'll keep flowering for longer.

Clip it over with shears to deadhead and reshape, taking an inch of leafy growth at the same time, every time you want to take flowers off - that should help them keep a good shape and put off the formation of a lot of wood.