Paladin and rogue in the same group - what's allowed and what's not?

[Rorrik]

"There is truly only the barest glimmer of hope"
or
"only a naive fool would try to convert them"

might justify not trying to redeem a defeated "Always Evil-race opponent"- but it wouldn't justify killing one in itself. There needs to be a better reason, like

"it's committed acts that warrant the death penalty"
or
"it's in the process of harming innocents and the only way to stop it is to kill it"

I wanted to add to the two justifications "it is likely to go on to harm innocents(or regular folk if you don't believe in innocents)."

In the case of a red dragon, while it may not be burning the nearby village to the ground right now, there's no guarantee the good guys will be able to stop it when it is, if they are even in the area. While ideally it could be brought before a court the moment it commits a crime, D&D adventures tend to take place in the wild, beyond the long arm of the law itself. Out here on the raggedy edge, leaving a likely threat alive because you got to it before it got to you is Lawful Stupid.

By this token, I would not be averse to letting a paladin character go so far as to take part in an effort of a kingdom to kill all chromatic dragons in a nearby range of mountains on the justification of several villages at the base of the mountains being destroyed in recent months. Genocide? Maybe. I'd certainly be a little more queasy about it if the paladin were doing it to avenge his family, or because he hates dragons, or for renown. But if his motivation is to defend the innocent lives of his nation or to obey his just king, then he's got the green light from me.