I think this is Fusarium wilt and that it is caused by two things: too much moisture and bad drainage.It is a common soil fungus. What you can do is re-plant in a dryer spot or you could lift them, dig the holes a bit deeper, add a layer of grit (and some soil on top ) and re-plant.
Either way you cut the Lavender back to healthy growth and remove all the clippings. Remember to disinfect your secateurs.