Team formation tools assume instructors should configure the criteria for creating teams, precluding students from participating in a process affecting their learning experience. We propose LIFT, a novel learner-centered workflow where students propose, vote for, and weigh the criteria used as inputs to the team formation algorithm. We conducted an experiment (N=289) comparing LIFT to the usual instructor-led process, and interviewed participants to evaluate their perceptions of LIFT and its outcomes. Learners proposed novel criteria not included in existing algorithmic tools, such as organizational style. They avoided criteria like gender and GPA that instructors frequently select, and preferred those promoting efficient collaboration. LIFT led to team outcomes comparable to those achieved by the instructor-led approach, and teams valued having control of the team formation process. We provide instructors and designers with a workflow and evidence supporting giving learners control of the algorithmic process used for grouping them into teams.