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 10$^4$ times lower than the UV 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 timescale 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 which 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. ; Comment: 5 pages, 5 figures. Accepted for publication in MNRAS letters