We describe an experimental study of soft solids composed of micron-scale lipid bilayer vesicles that adhere to one another through electrostatic attraction to an oppositely charged polymer (PDADMAC). As the polymer concentration was increased, we found a fluid phase, a solid gel phase, and a gel composed of internally reorganized vesicles. Optical microscopy images showed a nearly close-packed structure of adhered vesicles that retained their closed-cell morphology. Shear rheology measurements showed that the gel phase is a solid with a modulus at the Pa scale and with linear response up to 70% strain. We found that the modulus depends on the energy per area of membrane-membrane adhesion but does not depend on the vesicle size. We further found that the gels survived osmotic stress or dilution of the adhering polymer but could be rapidly disrupted in response to the addition of strongly binding silica nanoparticles. These results demonstrate the potential for cell-sized lipid vesicles to form a solid platform that maintains the responsive properties of the membranes. Such materials may find applications as triggerable, protective coatings of delicate surfaces.