Yes, you can still cry even if you've lost an eye.
Even with the loss of an eye and the presence of a prosthetic, the tear ducts associated with the remaining eyelid and eye socket are still functional. This means that emotional tears, as well as tears produced to lubricate the remaining eye and socket, can still be generated. Tears are produced by glands in the eyelids, so even with a prosthetic eye, the remaining tear production system allows for crying. The source material confirms that even while wearing a prosthetic eye, crying is still possible.
