LB-1 has variously been proposed as either an X-ray dim B-type star plus black hole (B+BH) binary, or a Be star plus an inflated stripped star (Be+Bstr) binary. The Space Telescope Imaging Spectrograph (STIS) on board HST was used to obtain a flux-calibrated spectrum that is compared with non-LTE spectral energy distributions (SED) and line profiles for the proposed models. The Hubble data, together with the Gaia EDR3 parallax, provide tight constraints on the properties and stellar luminosities of the system. In the case of the Be+Bstr model we adopt the published flux ratio for the Be and Bstr stars, re-determine the Teff of the Bstr using the silicon ionization balance, and infer Teff for the Be star from the fit to the SED. We derive stellar parameters consistent with previous results, but with greater precision enabled by the Hubble SED. While the Be+Bstr model is a better fit to the HeI lines and cores of the Balmer lines in the optical, the B+BH model provides a better fit to the SiIV resonance lines in the UV. The analysis also implies that the Bstr star has roughly twice solar silicon abundance, which is difficult to reconcile with a stripped star origin. The Be star on the other hand has a rather low luminosity, and a spectroscopic mass inconsistent with its possible dynamical mass. The fit to the UV can be significantly improved by reducing the Teff and radius of the Be star, though at the expense of leading to a different mass ratio. In the B+BH model, the single B-type spectrum is a good match to the UV spectrum. Adopting a mass ratio of 5.1+/-0.1 (Liu et al., 2020ApJ...900...42L) implies a BH mass of 21^+9^_-8_ solar masses.