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We present new observations of the nebula around the Magellanic candidateLuminous Blue Variable S61. These comprise high-resolution data acquired withthe Australia Telescope Compact Array (ATCA), the Atacama LargeMillimetre/Submillimetre Array (ALMA), and VISIR at the Very Large Telescope(VLT). The nebula was detected only in the radio, up to 17 GHz. The 17 GHz ATCAmap, with 0.8 arcsec resolution, allowed a morphological comparison with theH$\alpha$ Hubble Space Telescope image. The radio nebula resembles a sphericalshell, as in the optical. The spectral index map indicates that the radioemission is due to free-free transitions in the ionised, optically thin gas,but there are hints of inhomogeneities. We present our new public code RHOCUBEto model 3D density distributions, and determine via Bayesian inference thenebula's geometric parameters. We applied the code to model the electrondensity distribution in the S61 nebula. We found that different distributionsfit the data, but all of them converge to the same ionised mass, ~0.1 $\rmM\odot$, which is an order of magnitude smaller than previous estimates. Weshow how the nebula models can be used to derive the mass-loss history withhigh-temporal resolution. The nebula was probably formed through stellar winds,rather than eruptions. From the ALMA and VISIR non-detections, plus the derivedextinction map, we deduce that the infrared emission observed by spacetelescopes must arise from extended, diffuse dust within the ionised region.

New ATCA, ALMA and VISIR observations of the candidate LBV SK-67266 (S61): the nebular mass from modelling 3D density distributions