.The continuous adiabatic demagnetization refrigerator (CADR) described in this paper is a compact, reliable, and highly efficient magnetic cooling system designed for the line emission mapper (LEM), a future x-ray probe mission currently being proposed. Operating at two distinct temperatures of 350 mK (T1) and 40 mK (T0), the CADR offers continuous cooling while efficiently rejecting heat to a cryocooler at 4 K. Shielded by ferromagnetic and high-permeability magnetic shields, the CADR minimizes interference on the focal plane assembly. With flight-proven components, the CADR provides precise temperature regulation via its sensitive and large-arrayed transition edge sensor detectors. The CADR system for LEM consists of two modular units. The high-temperature module spans from 4 K to 350 mK, comprising four stages, whereas the low-temperature module spans from 350 to 40 mK, comprising three stages. The system is designed to continuously deliver 174 μW of useful cooling power at 350 mK and 2 μW at 40 mK.