can these plants grow well together

You can. I've got them growing together. The Snow on the mountains tries to take over and grow up through the lavender so I have to keep on pulling it out to keep it under control. Mine is quite a big established lavender so it holds its own.

Dear Chrispook,
Thankyou for replying, i have a well established ground covering of snows, and i recently had a lavender cutting which i would like to put behind the snows. I was a bit worried that the snows would 'strangle' the lavender but you've put my mind at rest. All the best to you and thanks again. Ajn.