Lipid droplets (LDs) are intracellular organelles that act as reservoirs for energy homeostasis and phospholipid balance between supply and consumption. In comparison with extensive studies on LD biogenesis from a biological viewpoint, little is known about the mechanical interaction between LDs and vesicles. Here we perform a systematic theoretical study on the budding and morphological evolution of an artificial LD embedded within the lipid membrane of a pressurized vesicle. It is found that LD bulging and budding depend on the bending rigidity and spontaneous curvature of the vesicle membrane, LD-vesicle interfacial interaction energy strength and size ratio, and osmotic pressure of the vesicle. Beyond critical interfacial interaction strength, the embedded LD undergoes a discontinuous shape transition from a lens-shaped bulge to a spherical protrusion connecting to the nearly spherical vesicle lumen via an infinitesimally small monolayer neck. Moreover, a positive monolayer spontaneous curvature promotes budding transition. As the vesicle becomes smaller, higher cost of the monolayer stretching energy is required for an LD to achieve budding transition. Budding phase diagrams distinguishing the embedded and budding states of the LD-vesicle complex accounting for osmotic pressure and interfacial interaction strength are established with the budding transition boundary displaying a nonmonotonic feature. Our results reveal how embedded LDs overcome soft membrane confinement and protrude, and provide fundamental insights into the clustering of nanoparticles between vesicle monolayers.