We used a technique that allows us to visualize local and morphological changes of the membrane of more component giant unilamellar vesicles due to high pressure perturbation. Under these conditions, thermally induced processes are largely suppressed, and the bending rigidity and line tension are influenced by pressure-induced changes in lipid molecular packing and shape only. We studied the effect of pressure on the lateral organization and morphology of the model raft system DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine)/sphingomyelin/cholesterol as well as of the fluid mixture POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine)/DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine) by two-photon excitation fluorescence microscopy. The pressure-dependent experiments were carried out using a sample cell made from a thin fused silica capillary. The use of Laurdan as fluorescence label allowed us to also follow the lipid phase state by calculating the generalized polarization (GP) values of the vesicles and extracting their average value. During the compression cycle, a reduction in the volume of the vesicles is observed, accompanied by an increase of the average GP value, indicating an increasingly tighter packing of the lipids. Interestingly, the two systems studied show phenomena of budding and fission, and these at surprisingly low pressures of 200-300 bar. Moreover, these budding processes are not directly related to phase transitions to an overall ordered conformational state of the lipid membrane, which occur at much higher pressures. The topological changes of the lipid vesicles are irreversible and exhibit a different behavior depending on whether the pressure is increased or decreased. The results are discussed in light of the various contributions to the free energy functional of lipid vesicles. Finally, the biological relevance of these studies is highlighted.