Lightspeed Classroom does offer a solution for locking individual student's internet.

There are a couple of places where teachers can access class controls for a single student. On your class page, mouse over the student tile that you want to apply class controls. The student tile will be shaded blue and there will be an ellipsis menu in the top right of the tile. Click the ellipsis to expose the class controls menu. Lock Screen and Unlock Screen will be the first controls on the list.

You can also click the student tile to open up the Student Information Panel. In the upper right of the Student Information Panel Click the ellipsis to open the class controls for that student

Full documentation is available here: https://help.lightspeedsystems.com/s/article/Lock-Unlock-Screens-Classroom-v2