Earth's temporarily-captured orbiters (TCOs) are a sub-population of near-Earth objects (NEOs). TCOs can provide constraints for NEO population models in the 1–10-metre-diameter range, and they are outstanding targets for in situ exploration of asteroids due to a low requirement on Δv. So far there has only been a single serendipitous discovery of a TCO. Here we assess in detail the possibility of their discovery with the upcoming Large Synoptic Survey Telescope (LSST), previously identified as the primary facility for such discoveries. We simulated observations of TCOs by combining a synthetic TCO population with an LSST survey simulation. We then assessed the detection rates, detection linking and orbit computation, and sources for confusion. Typical velocities of detectable TCOs will range from 1∘/day to 50∘/day, and typical apparent V magnitudes from 21 to 23. Potentially-hazardous asteroids have observational characteristics similar to TCOs, but the two populations can be distinguished based on their orbits with LSST data alone. We predict that a TCO can be discovered once every year with the baseline moving-object processing system (MOPS). The rate can be increased to one TCO discovery every two months if tools complementary to the baseline MOPS are developed for the specific purpose of discovering these objects.