The high-pressure HP structural properties of Li2O are examined theoretically using first-principles calculations density-functional theory . The calculated results for the HP anticotunnite modification are compared to recent experimental studies. Our main focus is on the hexagonal Ni2In-type modification, which is a likely candidate for a HP phase of Li2O at pressures above 100 GPa. The structural aspects of a pressure-induced phase transition from anticotunnite to Ni2In are characterized in detail; the existence of precursor phenomena is pointed out.