Just like Grail power-ups vanish at the end of the day, so does Lust levels. The early levels are easy, and you should try doing as many many Experts and maybe even Ultimates while the level is low.

... well, I don't know how easy it'd be to a new player...

In any event, try to spend as much BP as possible on Lust while powering up through daily dungeons/disasters with AP. Good luck.