ABSTRACT We explore synergies between the Nancy Grace Roman Space Telescope and the Vera Rubin Observatory’s Legacy Survey of Space and Time (LSST). Specifically, we consider scenarios where the currently envisioned survey strategy for the Roman Space Telescope’s High Latitude Survey (HLS reference), i.e. 2000 deg2 in four narrow photometric bands is altered in favour of a strategy of rapid coverage of the LSST area (to full LSST depth) in one band. We find that in only five months, a survey in the W-band can cover the full LSST survey area providing high-resolution imaging for >95 per cent of the LSST Year 10 gold galaxy sample. We explore a second, more ambitious scenario where the Roman Space Telescope spends 1.5 yr covering the LSST area. For this second scenario, we quantify the constraining power on dark energy equation-of-state parameters from a joint weak lensing and galaxy clustering analysis. Our survey simulations are based on the Roman Space Telescope exposure-time calculator and redshift distributions from the CANDELS catalogue. Our statistical uncertainties account for higher order correlations of the density field, and we include a wide range of systematic effects, such as uncertainties in shape and redshift measurements, and modelling uncertainties of astrophysical systematics, such as galaxy bias, intrinsic galaxy alignment, and baryonic physics. We find a significant increase in constraining power for the joint LSST + HLS wide survey compared to LSST Y10 (FoMHLSwide = 2.4 FoMLSST) and compared to LSST + HLS (FoMHLSwide = 5.5 FoMHLSref).