The Liverpool Telescope is one of the world's premier facilities for time domain astronomy. The time domain landscape is set to radically change in the coming decade, with surveys such as LSST providing huge numbers of transient detections on a nightly basis; transient detections across the electromagnetic spectrum from other facilities such as SVOM, SKA and CTA; and the era of `multi-messenger astronomy', wherein events are detected via non-electromagnetic means, such as gravitational wave emission. We describe here our plans for Liverpool Telescope 2: a new robotic telescope designed to capitalise on this new era of time domain astronomy. LT2 will be a 4-metre class facility co-located with the LT at the Observatorio del Roque de Los Muchachos on the Canary island of La Palma. The telescope will be designed for extremely rapid response: the aim is that the telescope will take data within 30 seconds of the receipt of a trigger from another facility. The motivation for this is twofold: firstly it will make it a world-leading facility for the study of fast fading transients and explosive phenomena discovered at early times. Secondly, it will enable large-scale programmes of low-to-intermediate resolution spectral classification of transients to be performed with great efficiency. In the target-rich environment of the LSST era, minimising acquisition overheads will be key to maximising the science gains from any follow-up programme. The telescope will have a diverse instrument suite which is simultaneously mounted for automatic changes, but it is envisaged that the primary instrument will be an intermediate resolution, optical/infrared spectrograph for scientific exploitation of transients discovered with the next generation of synoptic survey facilities. In this paper we outline the core science drivers for the telescope, and the requirements for the optical and mechanical design.