Ah, at last a photograph. I'm sorry to tell you that Lavender is really only good for about five years, by which time its getting pretty woody. Regular clipping helps to keep it better for longer, but this clipping involves only taking an inch or so of growth each time. You cannot cut into old wood, it won't regrow and will likely kill the plant. I'm afraid those old, bare, woody stems will remain that way, with growth at the top only. If you want to replace them, consider widening the space available to them, so that you've enough room to allow for a rounded shape down to the ground. Taking some off the lawn would allow for this.

That's a pretty impressive lavender hedge, even with the problem. It must smell glorious walking past your house!

Take lots of cuttings and raise your own replacement hedge over the next couple of years ready to take over when the current hedge has done all it can.