The Line Emission Mapper (LEM) is a Probe mission concept developed in response to NASA's Astrophysics Probe Explorer (APEX) Announcement of Opportunity. The LEM project is a collaboration between the Smithsonian Astrophysical Observatory (SAO), the NASA Goddard Space Flight Center (GSFC) and Lockheed Martin (LM). LEM is a large field of view (30 ′ equivalent diameter), soft X-ray mission (0.2-2.0 keV bandpass) with a large format microcalorimeter X-ray imaging spectrometer in the focal plane (1.3-2.5 eV spectral resolution) that provides unprecedented grasp (the product of effective area times field of view) in this bandpass. LEM's sensitivity to diffuse X-ray emission will be orders of magnitude higher than existing or proposed missions. LEM's primary science will characterize the diffuse gas in the X-ray haloes in galaxies, the outskirts of galaxy clusters and the filamentary structures between these clusters, and in the Milky Way star formation regions and Galactic halo, and Galactic and Local Group supernova remnants. To accomplish these objectives, the LEM spacecraft and mission have been designed to perform long observations of relatively faint objects and to perform an All-Sky Survey. The science payload consists of a single X-ray mirror assembly and a single focal plane instrument, the microcalorimeter operating at a temperature of 40 mK. The LEM spacecraft is a high-heritage, low-risk design that meets or exceeds all requirements, in particular the thermal requirements for the calorimeter, electronics, and mirror. The science mission profile supports high observing efficiency (> 90%), large sky coverage (45 − 150 • field of regard), and flexible operations that maximize the science return. LEM mission and science operations follow the same successful approaches used by LM for 16 NASA missions and by SAO for 24 years of successful operation of a NASA Great Observatory, the Chandra X-ray Observatory. With multiple decades of experience developing and maintaining the Chandra X-Ray Center Data System, the LEM team will develop the software to produce and disseminate high-quality data to the entire astronomical community. In this paper, we discuss the design of the mission and spacecraft operations that supports the transformational science that LEM promises to deliver.