ABSTRACT We studied the spectral changes of the high-mass X-ray binary system LMC X-4 to understand the origin and mechanisms beyond its superorbital modulation (30.4 d). To this aim, we obtained a monitoring campaign with Swift/XRT (0.3–10 keV) and complemented these data with the years-long Swift/BAT survey data (15–60 keV). We found a self-consistent, physically motivated, description of the broad-band X-ray spectrum using a Swift/XRT and a NuSTAR observation at the epoch of maximum flux. We decomposed the spectrum into the sum of a bulk + thermal Comptonization, a disc reflection component, and a soft contribution from a standard Shakura–Sunyaev accretion disc. We applied this model to 20 phase-selected Swift spectra along the superorbital period. We found a phase-dependent flux ratio of the different components, whereas the absorption column does not vary significantly. The disc emission is decoupled with respect to the hard flux. We interpret this as a geometrical effect in which the inner parts of the disc are tilted with respect to the obscuring outer regions.