I called LSAC about this yesterday and they said the June 2021 LSAT is part of the previous cycle. The current cycle began in August 2021. So taking it in January2022 will be your 3rd exam of the cycle.
I always tell students to check the schools they are applying to. It doesn't matter if that date is fine for 99% of the schools if it's toolate for the one you want to go to. That being said, it should be OK for the vast majority.