Yes, lesser and lesser-platinum are the same.
A queen bee will take more than one generation to establish, unless you buy a bee right off the bat.
Spider x pastel = bee
bee x lesser = queen bee
Of course, there's no guarantees on hitting the odds, but that is how one goes about it. You could also do:
lesser x spider = lesser-bee
lesser-bee x pastel = queen bee
...or any similar combination. Obviously the quickest way would be to get a bee to start with.