Giving Lore to Another Character

Not 100% on this, but there might be battle event coding that affects who is removed from the party.

Yes you are right! There are actually two battle events to change, when Gau comes back after a battle and when he runs away after you hit him. It would still need to be tested but changing the actor ID on those two battle events should work.

Code:

[Gau appears on the Veldt after a battle]
D0A9F1: 0E            Clear animations
D0A9F2: 03 0B FE A9   Animation for character 1(GAU) at $D0A9FE
D0A9F6: 0F            Excecute animations
D0A9F7: 13 0B         Add actor $0B(GAU) as a taget
D0A9F9: 11            Open dialogue window at bottom of the screen
D0A9FA: 01 FE         Display long battle dialogue $FE at bottom of the screen
                         "GAU: Uwaoo~!!"
D0A9FC: 10            Close dialogue window at bottom of the screen
D0A9FC: FF            End of battle event

[Gau runs away after you hit him once]
D0B421: 0E            Clear animations
D0B422: 03 0B 36 B4   Animation for character 1(GAU) at $D0B436
D0B426: 0F            Excecute animations
D0B427: 11            Open dialogue window at bottom of the screen
D0B428: 01 39         Display long battle dialogue $39 at bottom of the screen
                         "GAU: Uwaou!! Waooo……ooo! You……strangers…! Go away! You scare animals"
D0B42A: 0E            Clear animations
D0B42B: 03 0B 55 B4   Animation for character 1(GAU) at $D0B455
D0B42F: 04 0B AB B4   Animation for character 2(GAU) at $D0B4AB
D0B433: 0F            Excecute animations
D0B434: 10            Close dialogue window at bottom of the screen
D0B434: FF            End of battle event

Taken from the battle events scripts available here.