Context. Dust grains play an important role in the synthesis of molecules in the interstellar medium, from the simplest species, such as H₂, to complex organic molecules. How some of these solid-state molecules are converted into gas-phase species is still a matter of debate. Aims. Our aim is to directly compare ice and gas abundances of methanol (CH₃OH) and carbon monoxide (CO) obtained from near-infrared (2.5−5 μm) and millimetre (1.3 mm) observations and to investigate the relationship between ice, dust, and gas in low-mass protostellar envelopes. Methods. We present Submillimeter Array (SMA) and Atacama Pathfinder EXperiment (APEX) observations of gas-phase CH₃OH (J_K = 5_K−4_K), ¹³CO, and C¹⁸O (J = 2−1) towards the multiple protostellar system IRAS 05417+0907, which is located in the B35A cloud, λ Orionis region. We use archival IRAM 30 m data and AKARI H₂O, CO, and CH₃OH ice observations towards the same target to compare ice and gas abundances and directly calculate CH₃OH and CO gas-to-ice ratios. Results. The CO isotopologue emissions are extended, whereas the CH₃OH emission is compact and traces the giant molecular outflow emanating from IRAS 05417+0907. A discrepancy between sub-millimetre dust emission and H₂O ice column density is found for B35A−4 and B35A−5, similar to what has previously been reported. B35A−2 and B35A−3 are located where the sub-millimetre dust emission peaks and show H₂O column densities lower than that of B35A−4. Conclusions. The difference between the sub-millimetre continuum emission and the infrared H₂O ice observations suggests that the distributions of dust and H₂O ice differ around the young stellar objects in this dense cloud. The reason for this may be that the four sources are located in different environments resolved by the interferometric observations: B35A−2, B35A−3, and, in particular, B35A−5 are situated in a shocked region that is plausibly affected by sputtering and heating, which in turn impacts the sub-millimetre dust emission pattern, while B35A−4 is situated in a more quiescent part of the cloud. Gas and ice maps are essential for connecting small-scale variations in the ice composition with the large-scale astrophysical phenomena probed by gas observations.