I tried this small scale test yesterday before making a bigger version.

I cut the same design from 3mm walnut plywood and 3mm birch plywood the only difference being making the design 0.1mm bigger for the second cut to try to account for the thickness of the laser beam and get a precise fit. 

It didn't turn out perfect but not bad for a first test.

I have included the XCS file and the original SVG of the lion incase anybody likes the design.