The solar outer atmosphere is an extremely dynamic environment characterized by the continuous interplay between the plasma and the magnetic field that generates and permeates it. Such interactions play a fundamental role in hugely diverse astrophysical systems, but occur at scales that cannot be studied outside the solar system. Understanding this complex system requires concerted, simultaneous solar observations from the visible to the vacuum ultraviolet (VUV) and soft X-rays, at high spatial resolution (between 0.1'' and 0.3''), at high temporal resolution (on the order of 10 s, i.e., the time scale of chromospheric dynamics), with a wide temperature coverage (0.01 MK to 20 MK, from the chromosphere to the flaring corona), and the capability of measuring magnetic fields through spectropolarimetry at visible and near-infrared wavelengths. Simultaneous spectroscopic measurements sampling the entire temperature range are particularly important. These requirements are fulfilled by the Japanese Solar-C mission (Plan B), composed of a spacecraft in a geosynchronous orbit with a payload providing a significant improvement of imaging and spectropolarimetric capabilities in the UV, visible, and near-infrared with respect to what is available today and foreseen in the near future. The Large European Module for solar Ultraviolet Research (LEMUR), described in this paper, is a large VUV telescope feeding a scientific payload of high-resolution imaging spectrographs and cameras. LEMUR consists of two major components: a VUV solar telescope with a 30 cm diameter mirror and a focal length of 3.6 m, and a focal-plane package composed of VUV spectrometers covering six carefully chosen wavelength ranges between 170 Å and 1270 Å. The LEMUR slit covers 280'' on the Sun with 0.14'' per pixel sampling. In addition, LEMUR is capable of measuring mass flows velocities (line shifts) down to 2 km s - 1 or better. LEMUR has been proposed to ESA as the European contribution to the Solar C mission.