Yes. Lab Admins can control whether a user should require admin/instructor approval for equipment bookings. This is controlled via the user's individual user settings, or in access group settings. Press edit on the user or access group that you want to make approval required for, then turn on the setting 'Do bookings from this user require approval?'.
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Now, when the user creates a booking on the calendar for an equipment with this access rule turned on, they will be creating a booking request that the admin or instructor for this equipment can approve or decline.
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Admins can see all booking requests by clicking on Equipment > Bookings on the left hand menu. Here Requests are marked with the yellow label.
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To approve or decline a booking, select the booking from the list, or you can click on the booking request directly from the lab calendar, and then from the booking details page you can approve/decline the booking.
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