  BL Lacertae (BL Lac) objects are a subclass of blazar, distinguished by their
featureless optical spectrum. The featureless spectrum presents a challenge in
measuring the redshift of the BL Lacs. In this paper, we measure the redshift
of BL Lacs using the photometric dropout technique. The space-based telescope
\emph{Swift} and the ground-based SARA telescopes are employed to provide
magnitudes in the $uvw2,\ uvm2,\ uvw1,\ u,\ b,\ v,\ g',\ r',\ i',\ z'$ filters.
We observe 60 BL Lacs and report reliable redshift upper limits for 41 of them.
We discover three new high-$z$ BL Lacs ($z>1.3$) at $1.74_{-0.08}^{+0.05}$,
$1.88_{-0.03}^{+0.07}$, and $2.10_{-0.04}^{+0.03}$, bringing the number of
high-$z$ BL Lacs found by this method up to 19. Discussions are made on the
implications for the blazar sequence, the \emph{Fermi} blazar divide, and the
gamma-ray horizon based on an analysis of the 4LAC catalog and all high-$z$ BL
Lacs found with the photo-$z$ technique.
