How is the lamb meat made in lamb gyros?
For the times I've done gyros as such, you basically make a 'paste' out of it in the food processor.

Throw ground lamb in and give it a whirl, mix your spices and such in, put it on a spit, fridge to give a bit hard, and then on the spit.  It comes out with a texture like that.  That's how that kind is often done.

For 'proper' tasting meat (more like the one on the left), its alternating layers of razor thin meat and fat.