Lensing flux-ratio anomalies have been frequently observed and taken as evidence for the presence of abundant dark matter substructures in lensing galaxies, as predicted by the cold dark matter (CDM) model of cosmogony. In previous work, we examined the cusp–caustic relations of the multiple images of background quasars lensed by galaxy-scale dark matter haloes, using a suite of high-resolution N-body simulations (the Aquarius simulations). In this work, we extend our previous calculations to incorporate both the baryonic and diffuse dark components in lensing haloes. We include in each lensing simulation: (1) a satellite galaxy population derived from a semi-analytic model applied to the Aquarius haloes; (2) an empirical Milky Way globular cluster population and (3) satellite streams (diffuse dark component) identified in the simulations. Accounting for these extra components, we confirm our earlier conclusion that the abundance of intrinsic substructures (dark or bright, bound or diffuse) is not sufficient to explain the observed frequency of cusp–caustic violations in the Cosmic Lens All-Sky Survey (CLASS). We conclude that the observed effect could be the result of the small number statistics of CLASS, or intergalactic haloes along the line of sight acting as additional sources of lensing flux anomalies. Another possibility is that this discrepancy signals a failure of the CDM model.