We present the design of mid-infrared and THz quantum cascade laser cavities formed from planar photonic crystals with a complete in-plane photonic bandgap. The design is based on a honeycomb lattice, and achieves a full in-plane photonic gap for transverse-magnetic polarized light while preserving a connected pattern for efficient electrical injection. Candidate defects modes for lasing are identified. This lattice is then used as a model system to demonstrate a novel effect: under certain conditions - that are typically satisfied in the THz range - a complete photonic gap can be obtained by the sole patterning of the top metal contact. This possibility greatly reduces the required fabrication complexity and avoids potential damage of the semiconductor active region.