The line emission mapper (LEM) is a probe-class mission concept that is designed to detect x-ray emission lines from hot ionized gas (T > 10⁶ K) that will enable us to test galaxy evolution theories. It will permit us to study the effects of stellar and black-hole feedback and flows of baryonic matter into and out of galaxies. The key to being able to study the hot gases that are otherwise invisible to current imaging x-ray spectrometers is that the energy resolution is sufficient to use cosmological redshift to separate extragalactic source lines from foreground Milky Way emission. LEM incorporates a large-format microcalorimeter array instrument called the LEM microcalorimeter spectrometer (LMS) with a light-weight x-ray optic with 10” half power diameter angular resolution. The LMS microcalorimeter array has pixels with 15″ pixel pitch over a 33′ field of view (FOV) optimized for the 0.3 to 2 keV energy band. The central 7′ region of the array has an energy resolution of 1.3 eV at 1 keV and the rest of the FOV has 2.5 eV energy resolution at 1 keV. The array will be read out with state-of-the-art time-division multiplexing. We present an overview of the LMS instrument, including details of the entire detection chain, the focal plane assembly, as well as the cooling system and overall mechanical and thermal design. For each of the key technologies, we discuss the current technology readiness level and the plan to advance them to be ready for flight. We also describe the current system design and our estimate for the mass, power, and data rate of the instrument. The design details presented concentrate primarily on the unique aspects of the LMS design compared with prior missions and confirm that the type of microcalorimeter instrument needed for LEM is not only feasible but also technically mature.