Lhotse is the fourth highest peak in the world and lies just south of Mount Everest; it's name even means "south peak" (lho = south, tse = peak). It is definitely considered a separate mountain, so it is a mistake to call it the "south peak of Everest". It rises almost 600m/2000' above the famous south col that connects Lhotse to Everest, an prominence value that would qualify any peak in the world for separate mountain status.
Few of the hundreds that slog up the south col/southeast ridge route on Everest every year have the energy or inclination to make a side-trip to Lhotse, but the route from the south col remains the most commonly used. A separate route altogheter is the south face of Lhotse, considered one of the great mountain walls of the Himalaya, challenging experienced mountaineers with over 3000m/10,000' of steep high-altitude rock climbing.