Both can be right, although I agree it's unlikely. Hopefully the authors of those two books will step in with more info, but I can provide some info on it.
Looking at FM:3145 it says the Federated Suns Lancers were expanded to a full brigade in 3132, not created in 3132. In fact the First Fed Suns Lancers LCT goes back to FM:3085 where it was an Independent Command. If you look back one page in FM:3145 you'll see the Independent Commands of 3145 featuring the First and Third Fed Suns Armored Cav and the First and Second New Ivaarsen Chasseurs. This shows that you can have multiples of a command without it being a full brigade or before it becomes a full brigade.
While it's possible, I agree in this case it seems odd or unlikely, simply because the units chosen for Historical: Wars of the Republic Era were the Third and Fourth Fed Suns Lancers. That would mean at least 3 independent commands prior to the full brigade being formed in 3132. But it's still possible since H:WoRE says both units suffered 70% casualties. Perhaps there were 3 independent commands, the First, Third, and Fourth and the Third and Fourth suffered so many losses in H:WoRE that they were dispersed into a new Second. Then later the Third and Fourth were reestablished when the brigade was created.
Hope that helps somewhat
