In terms of law versus chaos the D&D version tends to work on the basis of LN kind of being an absolutist judge type character. Functional at a divine level if the LN and CN deities are not in agreement they are definitely working at odds to each other. If they were neighbours then LN would be constantly filing complaints with the local ordnance council about CN doing anything, while CN would then be ignoring everything, playing their music really, really loud, and stealing LN's cat.

Best way to treat it is probably like LN being Mr Wilson and CN being Denis the Menace. Without Denis necessarily seeming to like Mr Wilson.