When selecting domains as Divine Strategist (Chaldira Zuzaristan) Luck is not available. It is clearly listed as one of her Domains (as is the subdomain Fate, and the unlisted Friendship subdomain). There are no restrictions with Divine Strategist. Removing the archetype does not fix this glitch.
See this site for Pathfinder content reference. http://www.pathfinderwiki.com/wiki/Chaldira_Zuzaristan
Okay, so this is a bit tricky. Halflings of Golarion lists the two halfling deities (Chaldira and Thamir), but references back to a 3.5 pathfinder book where Chaldira doesn't grant the luck domain. Now both deities have gotten a reprint in Inner Sea Gods (page 324/325, at the bottom) which adds the luck domain for Chaldira and the Nobility domain for Thamir. Now the PCGen source for Inner Sea Gods doesn't list any deities at all....
So I just had to double check to make sure I am not insane. This has been fixed already in https://pcgenorg.atlassian.net/projects/DATA/issues/DATA-2771 which added all of the deities listed in inner sea gods.
Must be fixed in RC3 then. So, you cancel the issue, duplicate fixed in version, and the tracker id.
I don't believe I can close/cancel an issue unless I've been struck with blindness/deafness and just cannot find the button.
Unconfirmed > Cancel. Looks like you can do that.