Brad's lip is bleeding because he has finally pushed Ray to violence. Ever since Ray told Brad he was thinking about leaving the Corps, Brad has been acting like a paranoid asshole. Like leaving the Marines means Ray's leaving Brad. As if. Brad is stuck with him for life, and he's had enough of the petty jabs. Nothing Brad says is going to push him away, and if he has to kick Brad's ass on a daily basis to make that sink in, so be it.