For the first time, lonsdaleite-rich impact diamonds from one of the largest Popigai impact crater (Northern Siberia) with a high concentration of structural defects are investigated under hydrostatic compression up to 25 GPa. It is found that, depending on the nature of a sample, the bulk modulus for lonsdaleite experimentally obtained by X-ray diffraction in diamond-anvil cells is systematically lower and equal to 93.3-100.5% of the average values of the bulk moduli of a diamond matrix. Density functional theory calculations reveal possible coexistence of a number of diamond/lonsdaleite and twin diamond biphases. Among the different mutual configurations, separate inclusions of one lonsdaleite (001) plane per four diamond (111) demonstrate the lowest energy per carbon atom, suggesting a favorable formation of single-layer lonsdaleite (001) fragments inserted in the diamond matrix. Calculated formation energies and experimental diamond (311) and lonsdaleite (331) powder X-ray diffraction patterns indicate that all biphases could be formed under high-temperature, high-pressure conditions. Following the equation of states, the bulk modulus of the diamond (111)/lonsdaleite (001) biphase is the largest one among all bulk moduli, including pristine diamond and lonsdaleite.