Luck has nothing to do with relics, relics needs commitment from each and every individual in a group that is pursing a relic, you have to be "so good" at the job you're getting the relic for to get pass the faction part of it.
The first part where you get the seals isn't about luck since they have a fair drop rate, me and my group once got 5 seals in 5 runs, without even having one in the top 20 list.
Then you have the 17 minutes speedrun, if you're skillful enough, all of you, you'll be able to get that in no time, unless if you Want to depend on luck and go for the bad drop rate by doing the normal speedrun.
During the faction, Ifrit and Garuda just pray that you won't be unlucky and get an error from the game
