You could also adopt a second deity that you come to revere over time, without necessarily having to reject your original. The closer the two deities are in relationship, portfolio and overall attitude, the smoother this could be.
Can you think of a common thread? Could the DM design part of the campaign that involve the churches of both groups?
You're going from Lawful Neutral to Lawful Good. Some possible overlaps might be in the area of Law, War and/or death. Should there be an event that would bring together the churches of both gods on a mutual purpose, you might develop respect for the other god without automatically rejecting your original.
A player in one of my games played a Favored Soul of Kord. Cool character. He died early in our game, and was Reincarnated by a Trent Druid as a Woodling. This Favored Soul never lost his devotion to Kord, but developed a respect for Obad-Hai, overlap was the realm of Hunting, Freedom, Combat, Strength. Later in the campaign, the church of Kord allied with withe Church of Bahamut to oppose a scheme of Tiamat. Kord's well known as a dragon hunter. Another player, a Warblade/Crusader who revered Kord, underwent the ritual of becoming a Dragonborn. The Favored Soul also developed a respect for Bahamut, while never diverting from his loyalty to Kord.