Weak spectral features in BL Lacertae objects ( BL Lac ) often provide a unique opportunity to probe the inner region of this rare type of active galactic nucleus . We present a Hubble Space Telescope /Cosmic Origins Spectrograph observation of the BL Lac H 2356-309 . A weak Ly \alpha emission line was detected . This is the fourth detection of a weak Ly \alpha emission feature in the ultraviolet ( UV ) band in the so-called “ high energy peaked BL Lacs ” , after Stocke et al . Assuming the line-emitting gas is located in the broad line region ( BLR ) and the ionizing source is the off-axis jet emission , we constrain the Lorentz factor ( \Gamma ) of the relativistic jet to be \geq 8.1 with a maximum viewing angle of 3.6 ^ { \circ } . The derived \Gamma is somewhat larger than previous measurements of \Gamma \approx 3 - 5 , implying a covering factor of \sim 3 % of the line-emitting gas . Alternatively , the BLR clouds could be optically thin , in which case we constrain the BLR warm gas to be \sim 10 ^ { -5 } M _ { \odot } . We also detected two H i and one O vi absorption lines that are within | \Delta v| < 150 km s ^ { -1 } of the BL Lac object . The O vi and one of the H i absorbers likely coexist due to their nearly identical velocities . We discuss several ionization models and find a photoionization model where the ionizing photon source is the BL Lac object can fit the observed ion column densities with reasonable physical parameters . This absorber can either be located in the interstellar medium of the host galaxy , or in the BLR .