  We report the results of eROSITA and NICER observations of the June 2020
outburst of the Be/X-ray binary pulsar RX J0529.8-6556 in the Large Magellanic
Cloud, along with the analysis of archival X-ray and optical data from this
source. We find two anomalous features in the system's behavior. First, the
pulse profile observed by NICER during maximum luminosity is similar to that
observed by XMM-Newton in 2000, despite the fact that the X-ray luminosity was
different by two orders of magnitude. By contrast, a modest decrease in
luminosity in the 2020 observations generated a significant change in pulse
profile. Second, we find that the historical optical outbursts are not strictly
periodic, as would be expected if the outbursts were triggered by periastron
passage, as is generally assumed. The optical peaks are also not coincident
with the X-ray outbursts. We suggest that this behavior may result from a
misalignment of the Be star disk and the orbital plane, which might cause
changes in the timing of the passage of the neutron star through the disk as it
precesses. We conclude that the orbital period of the source remains unclear.
