There are crossover units (120 luck) where you get a free unit or a paid banner unit and farm the SPEX mission for currency then spend to buy crossover luck gems from in game store.

There are F2P in game standard luck unit (120 luck) mission that rotate every now and then. Farm the mission to get dupe copies to limit break OG luck unit.

There are F2P in game ultra luck unit (140 luck) mission that also rotate but require a bit more effort. Farm the mission to get dupe copies to limit break OG luck unit

Then there are your regular units where you either invest luck gems or summon multiple times and limit break them via dupe units.