ABSTRACT In 2016, the first strongly lensed Type Ia supernova (SN Ia), iPTF16geu, at redshift z = 0.409 with four resolved images arranged symmetrically around the lens galaxy at z = 0.2163, was discovered. Here, refined observations of iPTF16geu, including the time delay between images, are used to decrease uncertainties in the lens model, including the the slope of the projected surface density of the lens galaxy, Σ ∝ r1 − η, and to constrain the universal expansion rate H0. Imaging with Hubble Space Telescope provides an upper limit on the slope η, in slight tension with the steeper density profiles indicated by imaging with Keck after iPTF16geu had faded, potentially due to dust extinction not corrected for in host galaxy imaging. Since smaller η implies larger magnifications, we take advantage of the standard candle nature of SNe Ia constraining the image magnifications, to obtain an independent constraint of the slope. We find that a smooth lens density fails to explain the iPTF16geu fluxes, regardless of the slope, and additional substructure lensing is needed. The total probability for the smooth halo model combined with star microlensing to explain the iPTF16geu image fluxes is maximized at 12 per cent for η ∼ 1.8, in excellent agreement with Keck high-spatial-resolution data, and flatter than an isothermal halo. It also agrees perfectly with independent constraints on the slope from lens velocity dispersion measurements. Combining with the observed time delays between the images, we infer a lower bound on the Hubble constant, $H_0 \gtrsim 40\, {\rm km \ s^{-1} Mpc^{-1}}$, at 68.3 per cent confidence level.