how do i remove kitchen sink drainer basket without a visible lock nut?
The entire lower plastic portion is the locknut.

Have a helper hold the strainer in place from above using a strainer wrench (it's a thing, sometimes called a spud wrench), or by jamming the handles of channellock pliers into it, while you get under there and unscrew the whole plastic body from the strainer (turn CCW if looking up at it from below).