We show how transitions between different Lifshitz phases in bilayer Dirac materials with and without spin-orbit coupling can be studied by driving the system. The periodic driving is induced by a laser and the resultant phase diagram is studied in the high frequency limit using the Brillouin-Wigner perturbation approach to leading order. The examples of such materials include bilayer graphene and spin-orbit coupled materials such as bilayer silicene. The phase diagrams of the effective static models are analyzed to understand the interplay of topological phase transitions, with changes in the Chern number and topological Lifshitz transitions, with the ensuing changes in the Fermi surface. Both the topological transitions and the Lifshitz transitions are tuned by the amplitude of the drive.
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