Three Mg II absorbers are presented, one of which is new (z = 1.340 in S5 0454+844), bringing the total number of Mg Ir systems in the 1 Jy radio-selected BL Lac sample to 10. Five of the 10 absorption systems are at W-lambda > 1 Angstrom; this is a factor of 4-5 greater than the number expected based upon quasar sight lines and is 2.5-3 sigma greater than the expectation value. Interpretations of this possible excess include either that some of the Mg II absorbers might be intrinsic to the BL Lac or that there is a correlation between the presence of absorbing gas in the foreground and the nearly featureless spectra of these BL Lac objects compared to quasars. Such a correlation can be created by gravitational microlensing as suggested by Ostriker & Vietri. The similarity between the optical spectra of BL Lac objects with Mg II absorption and the spectrum of the gamma-ray burst source GRB 970508 suggests that models of gamma-ray bursts as microlensed AGNs should be investigated.