The mass accretion rate is a crucial parameter for the study of the evolution of accretion discs around young low-mass stellar and substellar objects (YSOs). We revisit the case of MY Lup, an object where VLT/X-shooter data suggested a negligible mass accretion rate, and show it to be accreting on a level similar to other Class II YSOs in Lupus based on Hubble Space Telescope (HST) observations. In our HST-Cosmic Origins Spectrograph (HST-COS) and -Space Telescope Imaging Spectrograph (HST-STIS) spectra, we find many emission lines, as well as substantial far-ultraviolet (FUV) continuum excess emission, which can be ascribed to active accretion. The total luminosity of the C IV λ1549 Å doublet is 4.1 × 10⁻⁴ L_⊙. Using scalings between accretion luminosity, L_acc, and C IV luminosity from the literature, we derive L_acc ~2 × 10⁻¹ L_⊙, which is more than an order of magnitude higher than the upper limit estimated from the X-shooter observations. We discuss possible reasons for the X-shooter-HST discrepancy, the most plausible being that the low contrast between the continuum excess emission and the photospheric+chromospheric emission at optical wavelengths in MY Lup hampered detection of excess emission. The luminosity of the FUV continuum and C IV lines, strong H₂ fluorescence, and a “1600 A Bump” place MY Lup in the class of accreting objects with gas-rich discs. So far, MY Lup is the only peculiar case in which a significant difference between the HST and X-shooter Ṁ_acc estimates exists that is not ascribable to variability. The mass accretion rate inferred from the revisited L_acc estimate is Ṁ_acc ~ 1(_−0.5^+1.5) × 10⁻⁸ M_⊙ yr⁻¹. This value is consistent with the typical value derived for accreting YSOs of similar mass in Lupus and points to less clearing of the inner disc than indicated by near- and mid-infrared observations. This is confirmed by Atacama Large Millimeter Array (ALMA) data, which show that the gaps and rings seen in the sub-millimetre are relatively shallow.