I think that a LE priest of Haelyn has to be someone who is broadly advancing the agenda of Haelyn, but is willing to compromise the mercy, charity, and compassion in order to get the rest of the package: law, the social order, suppression of disorder, honor, grace, humility, nobility, courage would all still be in play. Such a priest would imagine (rightly or wrongly) that the times are desperate and the fight against chaos (perhaps Sarimie) and disorder calls for desperate measures and cruelty, inquisition, and dirty tricks are necessary to restore the upper hand to the forces of order.
A good character justifies killing and fighting by limiting combat to the code of chivalry, of which Haelyn is the source, and by only combating evil when necessary. The evil character fights for the code of chivalry, but only upholds part of it himself. He believes that he sacrifices his own honor for the greater good (and how much more lawful can you get?) by doing what no one else can do. Whether he fights chaos or evil, he fights fire with fire, using evil tactics so that the good people of Haelyn can sleep soundly in their beds, because he does the dirty work, assassinating, imprisoning the dangerous before they act, torturing and generally casting the net too widely and using the harshest methods to easily.
To make a good honor paradox, I’d make him someone who fights the good fight (the enemy he fights is a genuine enemy of Haelyn, real evil or chaos) but the methods he uses are seductive and unnecessary, almost Belinikian in their exultation of power over the defeated, and so the PC’s should wonder if its really desirable to defeat the bad guy. He should be effective at fighting the enemies of Haelyn, but at a high price. I’d also make him a bully and someone who would accept a tyranny of Haelyn as preferable to a loss. Perhaps (and again I don’t know who the other bad guys are in the campaign) he feels there have been too many losses already to the forces of Sarimie, or the abominations, or Medoere and Ruornil in the case of Diemed, guilders, or Belinik’s temples, and so on. Too many losses because we’ve been too gentle, too chivalrous, and the forces of law and good need him, and his black knights, to assist them so the rest of us can live in the light of good and law. He really would like to see law and goodness triumph, he’s just cutting corners.
As to drawing negative energy, I’d say yes. He’s corrupt and dark. He would not summon dark energy to combat good. He won’t raise undead to fight good aligned knights of Haelyn. But if he were combating an evil necromacer, he would say something like this as he uses his awe/command power “In life you were subject to the law, but the law still applies in death for the law is universal. OBEY! I command you, and serve Haelyn still in death, destroy this evil necromancer and do your duty even still.”
A lot of excellent stories of compromised values, honor paradoxes, and questions about whether evil in the service of good is actually true evil or tainted good. Could raise excellent moral debates within the party.