We describe the design of Lobster-ISS, an X-ray imaging all-sky monitor (ASM) to be flown as an attached payload on the International Space Station. Lobster-ISS is the subject of an ESA Phase-A study which will begin in December 2001. With an instantaneous field of view 162 x 22.5 degrees, Lobster-ISS will map almost the complete sky every 90 minute ISS orbit, generating a confusion-limited catalogue of ~250,000 sources every 2 months. Lobster-ISS will use focusing microchannel plate optics and imaging gas proportional micro-well detectors; work is currently underway to improve the MCP optics and to develop proportional counter windows with enhanced transmission and negligible rates of gas leakage, thus improving instrument throughput and reducing mass. Lobster-ISS provides an order of magnitude improvement in the sensitivity of X-ray ASMs, and will, for the first time, provide continuous monitoring of the sky in the soft X-ray region (0.1-3.5 keV). Lobster-ISS provides long term monitoring of all classes of variable X-ray source, and an essential alert facility, with rapid detection of transient X-ray sources such as Gamma-Ray Burst afterglows being relayed to contemporary pointed X-ray observatories. The mission, with a nominal lifetime of 3 years, is scheduled for launch on the Shuttle c.2009.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.