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 ( \sim 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 \geq 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 .