We model the radiatively driven flow from IM Lup – a large protoplanetary disc expected to be irradiated by only a weak external radiation field (at least 104 times lower than the ultraviolet field irradiating the Orion Nebula Cluster proplyds). We find that material at large radii (>400 au) in this disc is sufficiently weakly gravitationally bound that significant mass-loss can be induced. Given the estimated values of the disc mass and accretion rate, the viscous time-scale is long (∼10 Myr) so the main evolutionary behaviour for the first Myr of the disc's lifetime is truncation of the disc by photoevaporation, with only modest changes effected by viscosity. We also produce approximate synthetic observations of our models, finding substantial emission from the flow that can explain the CO halo observed about IM Lup out to ≥1000 au. Solutions that are consistent with the extent of the observed CO emission generally imply that IM Lup is still in the process of having its disc outer radius truncated. We conclude that IM Lup is subject to substantial external photoevaporation, which raises the more general possibility that external irradiation of the largest discs can be of significant importance even in low mass star forming regions.