The process in which an antigen-presenting cell expresses lipid antigen in association with an MHC class Ib protein complex on its cell surface, including lipid extraction, degradation, and transport steps for the lipid antigen both prior to and following assembly with the MHC protein complex. The lipid antigen may originate from an endogenous or exogenous source of lipid. Class Ib here refers to non-classical class I molecules, such as those of the CD1 family.