In free bilayers, the fluid to gel main phase transition of a monofluorinated phospholipid (F-DPPC) transforms a disordered fluid bilayer into a fully interdigitated monolayer consisting of ordered acyl tails. This transformation results in an increase in molecular area and decrease in bilayer thickness. We show that when confined in patches near a solid surface this reorganization proceeds under constraints of planar topography and total surface area. One consequence of these constraints is to limit the complete formation of the energetically favored, interdigitated gel phase. The noninterdigitated lipids experience enhanced lateral tension, due to the expansion of the growing interdigitated phase within the constant area. The corresponding rise in equilibrium transition temperatures produces supercooled lipids that vitrify when cooled further. Ultimately, this frustrated phase change reflects a coupling between dynamics and thermodynamics and gives rise to ail unusual phase coexistence characterized by the presence of two qualitatively different gel phases.