A Luck god would most likely be worshiped by Gamblers, Outlaws, and anyone who intends on finding patterns and meaning where there is no clear signs. I imagine the god itself would be a "Watcher," someone who takes great interest in the lives of mortals, and tipping the scales in their favor for meaningful events. I imagine his holy symbol would be a Tilted Scale. The worshipers would be "Seekers," trying to find the pattern of luck.

When "Using" luck, people tend to be trying to control it, gathering charms or performing routines. They would most likely have great sentiment for items that were with them during spectacular bouts of luck, which they would blame on the item itself. A compulsion to collect anything connected to any lucky event may be interesting: "The gambler trips on a stone just as an arrow flies at him, so he collects the stone and continues to run." They would similarly gather people who they considered lucky, and a Luck Cleric would most likely consider the people in their party to be a lucky charm.

The words "Unintentionally Successful" is how i would describe the domain. Their temples would most likely be accidentally founded on gold mines, and their clerics more-or-less fell into the position due to necessity. (Needed a place to hide, ran out of money and needed food/shelter) The religion wouldn't be large, as the only people who are lucky enough to benefit are people who the Luck God himself found interesting enough to influence, therefore many don't believe because they don't experience the luck promised. Still, the clerics would most likely distribute lucky charms they've gathered to townsfolk.

You wouldn't worship a god of luck at night, but only when you needed them. A prayer to the god of luck is a call for them to watch you, and an invitation to participate by tipping the scales: "Hey look over here at this one in a million shot!"

As for philosophies, they would most likely be emblematic of Kierkegaard's "Knight of Faith," believing that nothing is impossible through God. For this reason, they would attempt to slay dragons, attempt to marry a princess, or attempt any other normally impossible feat. They would also resign themselves to bad luck, and easily accept when something doesn't go their way. "Nothing is Impossible, but Come What May."

Hope this helps.