Liverpool John Moores University is currently conducting a feasibility study for a new 4m class robotic telescope, specialising in time domain astrophysics, to come into operation ~2020. This will be the successor to the existing 2m Liverpool Telescope currently in operation on La Palma. The time domain is set to become increasingly important with the advent of new facilities like LSST, SKA, Gaia and LOFT; which will detect huge numbers of variable stars, binaries and transients. It is also expected that in the next decade we will begin to detect astrophysical transients in more exotic ways, such as via gravitational waves or neutrino emission. The rapid response and flexibility of a robotic telescope makes it the ideal tool for probing the time variable sky. I will discuss the potential role for LT2 in the 2020+ time domain landscape, and the key science topics we hope to address.