While I know next to nothing about piezoelectrics and crystal cuts, I hope that I can help you a bit with the difference between non-leaky and leaky waves.
The basic solutions that you'll find in textbooks for Rayleigh waves assume that your solid medium is bounded by a vacuum on one side. That way, the boundary conditions are simpler, as the moving surface is not pushing against anything. Now, let's consider what happens if the other medium is not a vacuum but a fluid (i.e., a liquid or gas). The boundary conditions then require that the motion and mechanical stresses are the same at the boundary for both the solid and the adjacent fluid. In other words, the motion of the solid surface causes a motion in the fluid medium.
Now, even if you have a fluid medium adjacent to the solid, you don't necessarily have a leaky Rayleigh wave. For that to happen, the speed of the Rayleigh wave must be higher than the sound speed in the fluid medium. In that case, the fluid motion will be a plane wave propagating away from the solid, carrying some of the Rayleigh wave's energy away into the fluid. If the speed of the Rayleigh wave is lower than the speed of sound in the fluid, however, the fluid motion will be an evanescent wave that does not leak energy into the fluid. (As the Rayleigh wave has a frequency-dependent speed, this also means that there is a critical frequency at which the Rayleigh wave becomes leaky.)
Now, back to your crystal cuts. At a guess, I'd say that different crystal cuts give different Rayleigh wave speeds, and that the Rayleigh wave speeds for some cuts are higher than the speed of sound in a typical fluid medium (whatever "typical" means for your application), thus meaning that these cuts will more easily give you leaky surface waves.