Students are divided into two groups. One (1) of them begins to (2) repeat their new lesson with (3) teacher. The other one (4) review at the same time their old lessons with each other.
(1) Does "them" refer to groups, or to students? Formally, to "groups", of course, but still potentially unclear. Say "One group"
(2) You do not "repeat" a new lesson. Say "goes over". "Their" is poor: a group is "it", not "they". Say "the".
(3) Article required:
One group begins to go over the new lesson with the teacher.
EVEN BETTER is a complete revision:
The teacher presents a new lesson to one group.
(4) "Group" is singular. It either reviews "collectively" "the" (not "their") lessons, or the students in it review "their" lessons "with each other". "One" is not wrong, but for the sake of clarity "group" is better. "At the same time" should probably be put at the beginning, to enhance the contrast; or omitted altogether.
[At the same time,] the other group reviews the old lessons collectively.
[At the same time,] students in the other group review their old lessons with each other.
Student or Learner