There are several threads already covering this exact topic, so to the OP please search for existing threads before creating new ones.
One thing several of you seem to overlook is the fact that Lucius draws his 'ability' to 'resurrect' from Slaanesh. It is the Dark Prince's power and continued will that Lucius endure that enables Lucius to keep the cycle going. If Slaanesh was in a position where he was unable to revive Lucius (being too weak, or tiring of Lucius) then Lucius would likely just die and his soul consumed by Chaos.
For example, if Lucius tripped and drowned in a puddle (bit of a random example from the OP there!) where no one but himself was responsible, and where no one but himself felt any pang of emotion at his death, then technically, going literally by the 'rule' Lucius would simply die. But in this circumstance Slaanesh would likely have the ability and power to just repossess another Slaaneshi follower with Lucius' soul, so the cycle begins anew.
A better example in my eyes would be (as the above poster brought up) what if Lucius committed suicide? Well, taking into account that the reason Slaanesh starting bringing Lucius back in the first place (following his death at the hands of Lord Commander Cyrius) was because his 'agonising death was an experience of transcendent pleasure' and thus presumably Slaanesh wished it to occur again and again, because it likely pleased and empowered himself. Thus even if Lucius did commit suicide, it would still be an 'experience of transcendent pleasure' and thus Slaanesh would want to bring him back again. Although eventually the fickle Slaanesh will probably tire of Lucius and just let him die and consume his soul...
Is his resurrection ability completely unescapable? I mean, theoretically, if the Emperor killed him and was really happy over it would he turn into Lucius? Or would he be strong enough to deny Lucius his resurrection ability? And to a lesser extent, if someone like Eldrad killed him, or another character known for their epic abilities...
Or how about if Kharn/Typhus/Ahriman killed him? I imagine the chaos gods would have a minor fight over it and either Lucius would die or you'd end up with each god restoring their own favoured in some way... (in my opinion, that is)
I imagine it would depend on Slaanesh's current power and rankings within the Great Game. If the Emperor killed him for example, I highly doubt Slaanesh would be in a position to transform the Emperor into Lucius, the Emperor is simply too powerful and it would take so much energy, power and investment that Slaanesh would leave himself extremely vulnerable in the Great Game.
As for if a Champion of another Chaos God killed him (Eg. Kharn, Ahriman or Typhus), I think it largely depends on the Champions worth to their patron compared to Lucius' worth to Slaanesh, and the Champions patron's power and ranking within the Great Game compared to Slaanesh at that point. For example if Slaanesh was the dominant and most powerful Chaos God at the time of Lucius' death to (lets say) Kharn, and Slaanesh valued Lucius more than Khorne did Kharn, then Slaanesh would probably be in a position to revive Lucius at the expense of Kharn. This applies to the other gods and their champions as well in my mind.
