Lightning fate needs to spawn more often

[Melithea]

She spawns ever 2nd time the fate starts..

Though Lightning does seem to appear every other time the FATE pops. I'm assuming the same applies to all of the FATEs she appears in.

Not entirely true. There's actually two different versions of the FATE spawning on entirely different timers: The "normal" FATE and the event version. I've seen the two spawn a minute apart and I've seen the event FATE spawn twice in a row. On the plus side, this is great for incidental FATE farming if you have a low level class.