No Pulsar Companion Around the Nearest Low Mass White Dwarf

2MASS J050051.85$-$093054.9 is the closest known low-mass helium-core white dwarf in a binary system. We used three high-band international LOFAR stations to perform a targeted search for a pulsar companion, reaching sensitivities of ~3 mJy for a 10-ms pulsar at a DM = 1 pc$\cdot$cm$^{-3}$. No pulsed signal was detected, confidently excluding the presence of a detectable radio pulsar in the system.