Late-time observations of Type Ia supernovae (SNe Ia), >900 days after explosion, have shown that this type of SN does not suffer an "IR catastrophe" at 500 days as previously predicted. Instead, several groups have observed a slow-down in the optical light curves of these SNe. A few reasons have been suggested for this slow-down, from a changing fraction of positrons reprocessed by the expanding ejecta, through a boost of energy from slow radioactive decay chains such as 57Co --> 57Fe, to atomic "freeze-out." Discovering which of these (or some other) heating mechanisms is behind the slow-down will directly impact studies of SN Ia progenitors, explosion models, and nebular-stage physics. Recently, Graur et al. (2018) suggested a possible correlation between the shape of the late-time light curves of four SNe Ia and their stretch values, which are proxies for their intrinsic luminosities. Here, we present Hubble Space Telescope observations of the SN Ia ASASSN-14lp at ~850-960 days past maximum light. With a stretch of s = 1.15 +/- 0.05, it is the most luminous normal SN Ia observed so far at these late times. We rule out contamination by light echoes and show that the late-time, optical light curve of ASASSN-14lp is flatter than that of previous SNe Ia observed at late times. This result is in line with-and strengthens-the Graur et al. (2018) correlation, but additional SNe are needed to verify it.