I'm not aware of a way to drop different assignment groups for different students, however the is a way that this could be done just a bit differently:
Have a module for each lab, instead of an assignment group that students can see. The advantage of using modules is that you can also link pages and files with instructions and supporting information, and it frees assignment groups to be used for organizing the grades.
Then in your assignment groups put all of the graded assignments into a group together and set that to drop the lowest score. If your class has more than one graded assignment per lab, this will mean it is possible for the dropped assignments to come from different labs, but it will still only be one dropped from each assignment group and you can cluster the groups by type. (So if each lab has a quiz and a report to turn in, you would have a group for quizzes and a group for reports, and students might have the lab 1 quiz and lab3 report dropped.)
The only additional challenge is if you do not have the same activities, individually worth the same number of points, in each lab. In that case you would be back to needing groups for each lab and manually dropping one of those groups. If that applies to you, you might want to add your use case description to: https://community.canvaslms.com/t5/Idea-Conversations/Gradebook-Assignment-Groups-within-Groups/idi-...
You might also appreciate the discussion here: https://community.canvaslms.com/t5/Idea-Conversations/assignment-weighting-in-assignment-groups/idi-...
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