I read it as a choice: The other person dies, and you live ... or you both die. Not a simple swap lives. For a lawful character it makes perfect sense to swap one person's life for two. So a lawful good character is conflicted. Thus I would not say this is a definite no-no.
As Gygax defines Lawful Good in his DMG, it is Benthamite utiltarianism - the greatest good to the greatest number, or as Gygax puts it "whatever brings the most benefit to the greatest number of decent, thinking creatures and the least woe to the rest."
However, paladins are an obviously non-utilitarian archetype: they evoke a morality of duty and an ethic of honour, not the "shopkeeper's morality" of Benthamism.
This is one instance of the more general point that Gygax lumps all standard approaches to morality - human rights, wellbeing, duty, honour, consequentialism - under the label "good" and leaves the details as something to be sorted out on a table-by-table basis.
That's one reason why looking to the alignment descriptors to try and resolve these sorts of paladin questions is largely fruitless. A Benthamite paladin is anachronistic and (in my view) aesthetically jarring; others might disagree; but either way it's not something the rules answer for us.
As another poster said, don't make it a moral issue. Instead just look at the god they serve and ask yourself what they would think. It's basically the FRP equivalent to a standard Christian morality question -- don't consider the intrinsic morality or try and work it out from ethical principles, just go with "What Would Jesus Do?". So ... what would Pelor do?
To me this is fine if the player gets to decide what Pelor would do. But at many tables the assumption will be that Pelor is the GM's NPC and hence this is really the player asking the GM how to play his/her PC - which I think is a pretty degenerate state of affairs in a RPG.
The problem only gets worse if the GM then tries to answer the question of what Pelor would do by (i) looking up Pelor's alignment (NG?) and then (ii) trying to interpret the alignment principles - because as per the earlier part of my post, those principles provide no answers to these sorts of questions.
One thing to be careful about is that Paladins are not the exemplars of goodness. Because they serve both good and the law, they are always in conflict. If they are faced with choosing between evil and chaos, there is no strong reason why they wouldn't decide to do the evil lawful thing rather than the chaotic good thing.
Your Neutral Good priest is not so conflicted. Trust her ahead of paladins.
This I don't agree with. It's an idea that is incipient in Appendix IV of Gygax's PHB, is hinted at in the Manual of the Planes but that comes fuly into its own with Planescape. I think its incoherent.
It's clear in Gygax's alignment descriptions (in his PHB and DMG) that LG isn't some "diluted" form of good. LG persons aspire to be maximally good, and believe that
law (whatever exactly that means) is an essential means thereto. Conversely, the CG also aspire to be maximally good, but they believe that individual self-realisation rather than social order is the best means thereto. That is, the disagreement between LG and CG is not about whether law is intrisincally valuable but rather about whether it is a means or an osbtacle to realising truth, beauty, wellbeing etc.
The incoherence that reaches its pinnacle in Planescape is the following: that the Seven Heavens, Elys8um and Olympus are all
in some sense good. If the convictions of the LG, as presnted by Gygax in his alignment descriptions, are correct then it is impossible that Olympus should realise the good; and mutatis mutandis for the CG and the Seven Heavens. The way that Planescape deals with this is by decreeing that both Oympus and the Seven Heavens realise good to some degree, but that in each case its diluted by another value - Law or Chaos. And then Elysium gets presnted as purely or maximally good.
Not only does this contradict the alignment descriptions - which is one source of incoherence - but it makes no sense on its own terms. Because if pursing law and order
dilutes goodness then what rational person woudl possibly do that?!