The laser just by the inherent nature of how the systems work will probably warp the lens when you burn off the extra material to leave a lip for the ring effect.

What about a flat neon lens with simply a laser-etched "line" instead of a full "mesa" cutaway?

Isn't that neon material meant to be able to have etched lettering that seems to light up when side-lit? I don't think it would take that deep of a cut to make a visible glowing line in the neon material.