There can be different suggestions depending on which stability you wish to characterise (and the type of the particles).

If chemical - then corresponding spectra, oxidative titration, zeta potential, bending elasticity of the liposomes (reflects chemical condition), concentration of the lipid after extraction plus many other options.

If physical stability: then size and distribution of the suspension (Zetasizer; size-exclusion chromatography; SEM-TEM-optical +++).