There generally always is a rate-up...or has been anyway, except for maybe couple days here and there inbetween events. If you're f2p then I would definitely advise to pick and choose when to do daily pulls as that 250 lapis adds up quick.
You can get 100+40 (from pvp) lapis per day and then 300 from weekly challegen events, I think. Other than that completing stage challenges nets you a nice chunk of lapis as well.
There will be a nico stream tomorrow and I'm assuming other than announcing new event/content/characters they will probably also hand out some tickets. Not sure if all newly created accounts will get those tickets, but it might be worthwhile to consider rerolling/starting then.
The current rate-up characters are rather underwhelming, but I have big hopes for what's next, as Sakaguchi will be a guest on the nico stream tomorrow.