Its always struck me how easy LG & CG find ways of working together, but LG & LE seem destined for battle....
I can imagine a lawful empire, with a paladinic / monkish police force, where the jails were run by devils as part of 'just punishment'. the paladins would disagree with the methods of the devils, but couldn't disapprove of the aims. the devils would respect the paladins organisation, but despair of their lack of true efficiency. The inevitables acting as judges woudl carefully balance all facts before issuing their (final) judgement. Citizens contributing to the empire would find it an efficient, safe place to live. Dissenters would be warned, and finally compelled to obey the norms.
on the fringes are the woodlands, mystically protected by ancient elven bards who allow all and sundry to seek shelter in the lands. The orcs tribes are the defenders of the land, working with some human barabarian tribes, summoning demons and eladrim to defeat the imperial armies that threaten to invade. Meanwhile the underground halfling railroad provides a haven for escaped slaves and 'The Council of the Woods', a secret society allegedly works for the overthrow of the Empire and the establishment of Democratic city states.