Not if you want the lavender to survive! You will need to pull out.

Especially with the weed membrane--the weeds are probably coming up right next to the Lavenders. Not much chance of separating them with cardboard, as is usually recommended.

If it is at all possible for you to do you could try my method carefully. Cut the bottom off a pop or milk bottle, carefully thread the weed into the neck of the bottle and spray into the bottle, or you can do it with a carrier bag and a small notch in the bottom for the weeds.

Have you tried dabbing the weedkiller on with an old paintbrush or toothbrush, on to the leaves? I find that works on weeds that are a bit close to plants to be dug out.

Dabbing weedkiller onto dock leaves is a good idea, but once you have got that close to chickweed and grass you might just as well pull it out.

One of the reasons I don't like weed suppressant membrane is the problem of the weeds growing up through the hole you cut for the plant, that and the fact the stuff rots after a few years and looks awful. I am not saying others should not use just my opinion - I prefer a good deep layer of mulch.

I sort of agree with you Moongrower - its definitely an imperfect solution, its actually easier to weed with a hoe while they seedlings are young around an area without membrane present. Best use for it, and then it has to be heavier duty, is under gravel and pebbles.