  The Line Emission Mapper (LEM) is an X-ray Probe with with spectral
resolution ~2 eV FWHM from 0.2 to 2.5 keV and effective area >2,500 cm$^2$ at 1
keV, covering a 33 arcmin diameter Field of View with 15 arcsec angular
resolution, capable of performing efficient scanning observations of very large
sky areas and enabling the first high spectral resolution survey of the full
sky. The LEM-All-Sky Survey (LASS) is expected to follow the success of
previous all sky surveys such as ROSAT and eROSITA, adding a third dimension
provided by the high resolution microcalorimeter spectrometer, with each 15
arcsec pixel of the survey including a full 1-2 eV resolution energy spectrum
that can be integrated over any area of the sky to provide statistical
accuracy. Like its predecessors, LASS will provide both a long-lasting legacy
and open the door to the unknown, enabling new discoveries and delivering the
baseline for unique GO studies. No other current or planned mission has the
combination of microcalorimeter energy resolution and large grasp to cover the
whole sky while maintaining good angular resolution and imaging capabilities.
LASS will be able to probe the physical conditions of the hot phases of the
Milky Way at multiple scales, from emission in the Solar system due to Solar
Wind Charge eXchange, to the interstellar and circumgalactic media, including
the North Polar Spur and the Fermi/eROSITA bubbles. It will measure velocities
of gas in the inner part of the Galaxy and extract the emissivity of the Local
Hot Bubble. By maintaining the original angular resolution, LASS will also be
able to study classes of point sources through stacking. For classes with
~$10^4$ objects, it will provide the equivalent of 1 Ms of high spectral
resolution data. We describe the technical specifications of LASS and highlight
the main scientific objectives that will be addressed. (Abridged)
