If a character has committed some sort of major crime ( e.g. battery / murder / POSSIBLY theft ) and has full tradition, they should still lose LP upon death, otherwise we'll end up with an army of dedicated theft alts with full tradition. Possibly 20% loss for each instance of murder committed within the past 48 hours, if they're summoned with a murder smell, and a similar sort of loss for other crimes. ( I'd suggest 4% for each theft. )
Calculated after tradition, of course.