I'm just making conversation on a slow weekend here, so....
I guess we coud say that as far as the lottery goes (the people runing any specific lottery) it's only a quick pick if the ticket says QP, but as far as the players are concenred, any numbers chosen by any type of RNG is a QP.
"The Quick Pick Dating Service" - now that's an idea!
"How'd you guys meet?"
"Oh, he / she was a quick pick, we've been living together for five years now."