Using ab initio calculations, we investigate the effect of hydrostatic pressure on the electronic structure of LaMnO3 (111) bilayers sandwiched between LaAlO3. In the ideal heterostructure we observe Dirac cones at the Fermi energy. However, octahedral tiltings open a band gap and thus destroy the Dirac nature. We show that the effect of the tiltings can be suppressed by hydrostatic pressure from 40 GPa to 60 GPa. At higher pressure further phase transitions are encountered.