We present Hubble Space Telescope (HST) observations of seven unusual objects from the HST ``snapshot survey'' of BL Lacertae objects, of which four are gravitational lens candidates. In three cases a double point source is observed: 0033+595, with 1.58" separation, and 0502+675 and 1440+122, each with ~0.3" separation. The last two also show one or more galaxies, which could be either host or lensing galaxies. If any are confirmed as lenses, these BL Lac objects are excellent candidates for measuring H_0 via gravitational time delay because of their characteristic rapid, high-amplitude variability. An additional advantage is that, like other blazars, they are likely superluminal radio sources, in which case the source plane is mapped out over a period of years, providing strong additional constraints on the lensing mass distribution. The fourth gravitational lens candidate is 1517+656, which is surrounded by three arclets forming an almost perfect ring of radius 2.4". If this is indeed an Einstein ring, it is most likely a background source gravitationally lensed by the BL Lac object host galaxy and possibly a surrounding group or cluster. In the extreme case that all four candidates are true lenses, the derived frequency of gravitational lensing in this BL Lac sample would be an order of magnitude higher than in comparable quasar samples. We also report on three other remarkable BL Lac objects: 0138-097, which is surrounded by a large number of close companion galaxies; 0806+524, whose host galaxy contains an uncommon arclike structure; and 1959+650, which is hosted by a gas-rich elliptical galaxy with a prominent dust lane of ~5x10^5 M_solar.