Luxu did not take over Brain. As others have pointed out, the face reveal scene is from just after the War, the time when Brain and the others were starting as the new leaders. The only way this makes sense is if Luxu is time-traveling Brain from the future. He ended up in Scala at some time in the future (not very far forward, maybe a few decades or so), started a family there to become Eraqus's ancestor, then went back to the time before the War and became one of MoM's disciples.
So, two of my top four favorite characters are in fact one and same. And the information to find this out was available, in fact I see now that at one point I was one connection away from understanding it. Mind blown... 🥴