  Using data from eROSITA, the soft X-ray instrument aboard
Spectrum-Roentgen-Gamma (SRG), we report the discovery of two new hard
transients, eRASSU J050810.4-660653 and eRASSt J044811.1-691318, in the Large
Magellanic Cloud. We also report the detection of the Be/X-ray binary RX
J0501.6-7034 in a bright state. We initiated follow-up observations to
investigate the nature of the new transients and to search for X-ray pulsations
coming from RX J0501.6-7034. We analysed the X-ray spectra and light curves
from our XMM-Newton observations, obtained optical spectra using the South
African Large Telescope to look for Balmer emission lines and utilised the
archival data from the Optical Gravitational Lensing Experiment (OGLE) for the
long-term monitoring of the optical counterparts. We find X-ray pulsations for
eRASSU J050810.4-660653, RX J0501.6-7034, and eRASSt J044811.1-691318 of 40.6
s, 17.3 s, and 784 s, respectively. The Halpha emission lines with equivalent
widths of -10.4 A (eRASSU J050810.4-660653) and -43.9 A (eRASSt
J044811.1-691318) were measured, characteristic for a circumstellar disc around
Be stars. The OGLE I- and V-band light curves of all three systems exhibit
strong variability. A regular pattern of deep dips in the light curves of RX
J0501.6-7034 suggests an orbital period of ~451 days. We identify the two new
hard eROSITA transients eRASSU J050810.4-660653 and eRASSt J044811.1-691318 and
the known Be/X-ray binary RX J0501.6-7034 as Be/X-ray binary pulsars.
