To some extent phonons are already condensed. Usually they are thought of as the Goldstone modes of broken translational symmetry (ignore optical modes for simplicity). This means the superflow of phonons is constant movement of the crystal itself. In other words, the crystal can move at a constant velocity indefinitely (assuming no outside forces at work). In the torus geometry, the entire crystal will rotate indefinitely without dissipation.
However, I believe what you are really interested in is Bose condensation of the nuclei of the lattice themselves. This is actually what Ultracold atom people achieve regularly. However in their case they are dealing with gases, not solids!
But can you actually see this in a normal solid (say Lithium?)
The answer is probably yes in theory, but in practice it is no. As a rule of thumb for bose condensation, you need to have the thermal de Broglie wavelength of the atoms be at least on the order of the atomic spacing itself. For electrons, this is achieved trivially even at extremely high temperatures because of their tiny mass. However for nuclei, which have masses that are thousands of times heavier, this temperature would need to be in the nano kelvins at the highest (pico kelvin in reality). At that point, you could possibly get in the regime of atomic condensation, but usually you need to get even colder.
Currently, the coldest you can get a solid is in the milli to (high) micro kelvin regime. Getting into nano or pico kelvin is completely out of reach for an ordinary solid. Perhaps it will be possible in the future someday.