Re the name Limassol, or Limasol, according to the official site of the town municipality, Constantine Porhyrogennitos referred to the town as Nemesos, and that was back in the 10th century. It was called Theodosiani and then Neapolis before that. From Nemesos it is easy to figure out how Lemesos and then Limasol came about. So Lemesos is a lot closer to the original Nemesos than the latinish sounding Limasol.
Maybe someone will come up with a theory how the production of Lima beans in the area and the sunny climate gave rise to Lima Sol!