if that is the case, does it mean that we can summit two 8000ers at one go? summit Lhotse, then Everest or vice versa.
No one has ever climbed Lhotse via the South Col. The route is too difficult. You would have to descend and climb the couloir above the Lhotse Face.
You need to go back down to basecamp if you want the second summit to count (technically, because you would still be standing on top of the mountain!!!).
I disagree. You would have to descend down the Lhotse Face quite aways from the South Col anyway to climb Lhotse, and if you did do it from the South Col, you would have solved one of the problems on the "Everest Horseshoe". Anyone doing that deserves a huge amount of credit and could certainly count it.