We report on an X-ray polarimetric observation of the high-mass X-ray binary LMC X-1 in the high/soft state, obtained by the Imaging X-ray Polarimetry Explorer (IXPE) in October 2022. The measured polarization is below the minimum detectable polarization of 1.1 per cent (at the 99 per cent confidence level). Simultaneously, the source was observed with the NICER, NuSTAR and SRG/ART-XC instruments, which enabled spectral decomposition into a dominant thermal component and a Comptonized one. The low 2-8 keV polarization of the source did not allow for strong constraints on the black-hole spin and inclination of the accretion disc. However, if the orbital inclination of about 36 degrees is assumed, then the upper limit is consistent with predictions for pure thermal emission from geometrically thin and optically thick discs. Assuming the polarization degree of the Comptonization component to be 0, 4, or 10 per cent, and oriented perpendicular to the polarization of the disc emission (in turn assumed to be perpendicular to the large scale ionization cone detected in the optical and radio bands), an upper limit to the polarization of the disc emission of 0.5, 1.7, or 3.6 per cent, respectively, is found (at the 99 per cent confidence level).