The interplay between magnetism and superconductivity in LaFeAsO0.945F0.055 was studied as a function of hydrostatic pressure up to p=2.4 GPa by means of muon-spin rotation (μSR) and magnetization measurements. The application of pressure leads to a substantial decrease of the magnetic ordering temperature, reduction of the magnetic phase volume and, at the same time, to a strong increase of the superconducting transition temperature and the diamagnetic susceptibility. From the volume-sensitive μSR measurements it can be concluded that the superconducting and the magnetic areas, coexisting in the same sample, are inclined toward spatial separation and compete for phase volume as a function of pressure.