Bright submillimetre-selected galaxies have been found to be a rich source of strong gravitational lenses. However, strong gravitational lensing of extended sources leads inevitably to differential magnification. In this paper I quantify the effect of differential magnification on simulated far-infrared and submillimetre surveys of strong gravitational lenses, using a foreground population of Navarro–Frenk–White plus de Vaucouleurs’ density profiles, with a model source resembling the Cosmic Eyelash and quasi-stellar object J1148+5251. Some emission-line diagnostics are surprisingly unaffected by differential magnification effects: for example, the bolometric fractions of [Cii] 158 μm and CO(J = 1 − 0), often used to infer densities and ionization parameters, have typical differential magnification effects that are smaller than the measurement errors. However, the CO ladder itself is significantly affected. Far-infrared lensed galaxy surveys (e.g. at 60 μm) strongly select for high-redshift galaxies with caustics close to active galactic nuclei (AGNs), boosting the apparent bolometric contribution of AGN. The lens configuration of IRAS F10214+4724 is naturally explained in this context. Conversely, submillimetre/millimetre-wave surveys (e.g. 500–1400 μm) strongly select for caustics close to knots of star formation boosting the latter's bolometric fraction. In general, estimates of bolometric fractions from spectral energy distributions of strongly lensed infrared galaxies are so unreliable as to be useless, unless a lens mass model is available to correct for differential magnification.