/ AbstractThe Line Emission Mapper's (LEM's) exquisite spectral resolution and effective area will open new research domains in Astrophysics, Planetary Science and Heliophysics. LEM will provide step-change capabilities for the fluorescence, solar wind charge exchange (SWCX) and auroral precipitation processes that dominate X-ray emissions in our Solar System. The observatory will enable novel X-ray measurements of historically inaccessible line species, thermal broadening, characteristic line ratios and Doppler shifts - a universally valuable new astrophysics diagnostic toolkit. These measurements will identify the underlying compositions, conditions and physical processes from km-scale ultra-cold comets to the MK solar wind in the heliopause at 120 AU. Here, we focus on the paradigm-shifts LEM will provide for understanding the nature of the interaction between a star and its planets, especially the fundamental processes that govern the transfer of mass and energy within our Solar System, and the distribution of elements throughout the heliosphere. In this White Paper we show how LEM will enable a treasure trove of new scientific contributions that directly address key questions from the National Academies' 2023-2032 Planetary Science and 2013-2022 Heliophysics Decadal Strategies. The topics we highlight include: 1. The richest global trace element maps of the Lunar Surface ever produced; insights that address Solar System and planetary formation, and provide invaluable context ahead of Artemis and the Lunar Gateway. 2. Global maps of our Heliosphere through Solar Wind Charge Exchange (SWCX) that trace the interstellar neutral distributions in interplanetary space and measure system-wide solar wind ion abundances and velocities; a key new understanding of our local astrosphere and a synergistic complement to NASA IMAP observations of heliospheric interactions...