Trying to divide a lavender plant would be like trying to cut a tree into vertical sections, from top right down to the bottom-most roots. Neither practical nor likely to be successful.

Your best way to propagate new plants is to take cuttings. I find that heel cuttings are best and easiest with lavender.

So I take it that's a no... :)

What exactly is a heel cutting and how do I go about getting one?

Take a healthy looking shoot which is about 10cm long and pull it down and away from the main stem. You will end up with a shoot which has a 'heel' of the main stem at its base. If the heel is a bit too long trim it with a sharp knife.

Dip the 'heel' in hormone rooting powder (better still, some pure honey), make a small hole in the potting mix with a pencil and place the cutting in the soil with the 'heel' lowermost. About 2-3cm of the cutting should be below the soil. Gently firm the soil down around the cutting. Keep the cuttings in a light airy position out of direct sunlight and keep the soil just moist.

The cutting should show some signs of growth in about 4-6 weeks.

Here is a link that might be useful: heel cuttings

Thank you :)