The central hallmark of Parkinson's disease pathology is the aggregation of the α-synuclein protein, which, in its healthy form, is associated with lipid membranes. Purified monomeric α-synuclein is relatively stable in vitro, but its aggregation can be triggered by the presence of lipid vesicles. Despite this central importance of lipids in the context of α-synuclein aggregation, their mechanistic role in this process has not been established to date. Here, we use chemical kinetics to develop a detailed mechanistic model that is able to globally describe the aggregation behaviour of α-synuclein in the presence of DMPS lipid vesicles, across a range of lipid and protein concentrations. Through the application of our kinetic model to experimental data, we find that the reaction is a co-aggregation process involving both protein and lipids and that lipids promote aggregation predominantly by enabling the elongation process. Moreover, we find that the initial formation of aggregates, via primary nucleation, takes place not on the surface of lipid vesicles but at the interfaces present in vitro. Our model will enable mechanistic insights, also in other lipid-protein co-aggregation systems, which will be crucial in the rational design of drugs that inhibit aggregate formation and act at the key points in the α-synuclein aggregation cascade.