It might just be me, but out of all the characters, Lann builds SP the fastest in Dragon. (I don't play a beast Fiona to compare, so I might be wrong.)
Honestly I think Fiona and Lann have about the same rate at which they gain SP. Usually I spend 1500-3000 SP on a Dragon run, but that includes holding onto SP while waiting for the Dragon to get shot down. The faster you use that SP, the faster you gain it back. Most Lanns seem content to use F7 as soon as they get 4 bars and instantly go back to gaining SP.