  A large fraction of black hole low-mass X-ray binaries (BHLMXBs) are in short
period orbits, which require strong orbital angular momentum loss during the
previous evolutionary stage. Ivanova (2006) put forward the possibility that
some of the BHLMXBs may harbour pre-main-sequence (MS) donor stars, in order to
explain the Li-overabundances in three BHLMXBs. In this work we investigate the
evolution of low-mass pre-MS stars in binaries with a BH companion. We
calculate the evolution of the spin and orbital periods, the stellar radius and
the Roche-lobe radius during the pre-MS stage with the stellar evolution code
MESA. We find that, because of the relatively slow rotation of the pre-MS star
after the common envelope evolution and the long turnover time in the pre-MS
stars, tidal torque is not always able to synchronize the pre-MS star, so the
spin periods are generally longer than the orbital periods. Mass transfer can
occur only for stars with mass larger than $\sim 1.2M_\odot$, which experience
expansion due to nuclear reaction after the Hayashi contraction phase. The
effective temperatures and orbital periods of these systems do not match the
observations of BHLMXBs. Our results show that the observed BHLMXBs with
lithium overabundances are unlikely to host pre-main sequence donor stars.
