According to this Youtube video, at 7:56, the narrator mentioned that after reaching Lhotse at 27,940 feet, climbers would hike back down to Base Camp (at 17,400 feet). If the climbers are already acclimatized to the high altitude, why do they go back down to Base Camp instead of going to the summit of Everest?
Some climbers do exactly that: climb to the Lhotse summit and then the Everest summit. They'd only do so after being fully acclimatized.
In this case, the video says "climbing a portion of Lhotse face for further acclimatization before returning all the way down to base camp." Every expedition uses a different acclimatization schedule, but they generally involve some number of partial ascents followed by a return to the lower elevation at base camp. The journey up the Lhotse face (which would be below 27,940 feet, it's part of the route to the Everest summit and the higher camps), would be part of the acclimatization process; the climbers are not "already acclimatized to the high altitude" and not yet prepared to summit.
In the video, I suspect they're talking about climbing above Camp II toward (or perhaps all the way to) Camp III, up the Lhotse face.