In episode 1 of season 3, why does Luther not want to arrest Ken. Would it not be more beneficial so that he can work on the other murder case?
As per IMDB, Luther sympathizes with Ken:
Prime suspect is Ken Barnaby, who was plagued by Cass with taunts over his dead daughter but Luther feels sorry for him, warning him of likely arrest which spurs Ken to take extreme action.
Luther is well known to go by his own compass more so than the rulebook. He didn't feel like Ken deserved to be arrested and thus warned him in advance so he could evade arrest.