It's a final sign of how utterly self-centered Jake is that he doesn’t even remember Lorena anymore. Although she pinned her hopes on him, she meant little to him other than the momentary pleasure she provided. Still, Jake salvages his dignity and his character somewhat in the end by spurring his own horse. By doing so, he avoids forcing his friends to execute him, and he takes responsibility for his actions—only tragically, it’s far too late to do him any good.