I've been watching the Justice League animated series and just watched the episode featuring the Justice Lords (A Better World - season 2, episodes 11 and 12). In it, the alternate version of the Justice League in an alternate universe hit a critical point in their history where they deviate from the attitude/mindset of the prime Justice League counterparts. They begin to resort to killing and/or adhoc medical procedures to suppress the criminal element on their Earth, and eventually dictating the rule of law.
Lord Green Lantern is in on this, and his combat style makes it clear that he uses more lethal attacks than other Green Lanterns we've seen in the prime universe. With the more lethal mindset and being directly involved in the suppression of a population, this would seem to be counter to the overall mission of the Green Lanterns which is presumably similar between the two universes.1
Ignoring the fact that the rest of the Green Lantern corp isn't doing anything about the situation, this got me thinking: the Green Lantern power rings seem to be semi-intelligent in that they choose their wielders. But once a power ring has chosen someone and ignoring death, can that ring then decide to leave that being if the being's nature changes? And if so, under what criteria would it be necessary for the ring to decide to leave?
1: This is an educated guess based on the introduction of Part 1 of A Better World. The opening scenes make it clear that the Justice Lords are operating about the same way as the Justice League when the episode starts. After some back and forth between one of the Lords and one of the supervillains, that Lord decides to resort to lethal force. This appears to be the moment where the Justice League and Justice Lords fork into very different mindsets when dispensing "Justice". Presumably, the Green Lantern power ring would have already chosen alternate John Stewart for similar reasons that prime John Stewart was also chosen.