There is strong experimental evidence of the influence of surfactants (e.g., fatty acids) on the kinetics of amyloid fibril formation. However, the structures of mixed assemblies and interactions between surfactants and fibril-forming peptides are still not clear. Here, coarse-grained simulations are employed to study the aggregation kinetics of amyloidogenic peptides in the presence of amphiphilic lipids. The simulations show that the lower the fibril formation propensity of the peptides, the higher the influence of the surfactants on the peptide self-assembly kinetics. In particular, the lag phase of weakly aggregating peptides increases because of the formation of mixed oligomers, which are promoted by hydrophobic interactions and favorable entropy of mixing. A transient peak in the number of surfactants attached to the growing fibril is observed before reaching the mature fibril in some of the simulations. This peak originates from transient fibrillar defects consisting of exposed hydrophobic patches on the fibril surface, which provide a possible explanation for the temporary maximum of fluorescence observed sometimes in kinetic traces of the binding of small-molecule dyes to amyloid fibrils.