I don't view LHO as a hero, however there are many ways to see any action.
LHO is often portrayed by LN's as a mean, wife beating jerk, but if he was indeed the shooter, the last action (for her) he did was give his separated wife his last possessions of any value, knowing that the money would come in handy if he wanted to flee the scene.
Furthermore the whole visit to the boarding room makes little sense. If he is the shooter on the run, why decide to go to a known abode to get changed, true he may have been going there to pick up the revolver (or he may already have had that) but then why get changed? The aimless erratic movement post shooting is either someone in panic (as opposed to his calmness on the 2nd floor) or someone who didn't expect to get out of the building alive.