Nuclear spin-lattice relaxation times are measured on copper using magnetic-resonance force microscopy performed at temperatures down to 42 mK. The low temperature is verified by comparison with the Korringa relation. Measuring spin-lattice relaxation times locally at very low temperatures opens up the possibility to measure the magnetic properties of inhomogeneous electron systems realized in oxide interfaces, topological insulators, and other strongly correlated electron systems such as high-Tc superconductors.@en