  L-type and T-type dwarfs span the boundaries between main-sequence stars,
brown dwarfs, and planetary-mass objects. For these reasons, L and T dwarfs are
the perfect laboratories for exploring the relationship between planet
formation and moon formation, and evidence suggests they may be swarming with
close-in rocky satellites, though none have been found to date. The discovery
of satellites orbiting L or T dwarfs will have transformative implications for
the nature of planets, moons and even life in the Universe. These transiting
satellites will be prime targets for characterization with NASA's James Webb
Space Telescope. In this white paper, we discuss the scientific motivations
behind searching for transiting satellites orbiting L and T dwarfs and argue
that robotizing current 1-to-2-meter US optical/infrared (O/IR) facilities and
equipping them with recently developed low-cost infrared imagers will enable
these discoveries in the next decade. Furthermore, robotizing the 1-to-2-meter
O/IR fleet is highly synergistic with rapid follow-up of transient and
multi-messenger events.
