It's hard to say for sure. It might have been that Jules saw something in LaVar Burton that made him reconsider. Or maybe external circumstances intervened and prevented the killing. Maybe it was to add complexity to Jules' character or to set up a future plot point.
Well, there could be multiple reasons. Maybe LaVar Burton did something to convince Jules not to. Or perhaps Jules had a moment of reflection and decided against it for personal or ethical reasons. Maybe it was part of a larger plot twist or character development.