1) Spend as much of your Kurzick faction as possible.
2) Do some quests that give Luxon faction points.
3) When your Luxon faction points > Kurzick faction points, you can speak to the Luxon merchants.
Yes, you have to complete the quest, "Befrending the Kurzick" whick requires 10k Kurzick Faction. Check the pinned Factions FAQ for the order of quests that you need to complete.
Basicly, your going to have to be Kurzick until you can get their armor, than you have to switch.