Unique spectroscopic possibilities open up if a laser beam interacts with relativistic lithium-like ions stored in the heavy ion ring accelerator SIS300 at the future Facility for Antiproton and Ion Research FAIR in Darmstadt, Germany. At a relativistic factor gamma = 36 the P-2(1/2) level can be excited from the S-2(1/2) ground state for any element with frequency doubled dye-lasers in collinear geometry. Precise transition energy measurements can be performed if the fluorescence photons, boosted in forward direction into the X-ray region, are energetically analyzed with a single crystal monochromator. The hyperfine structure can be investigated at the P-2(1/2)-S-2(1/2) transition for all elements and at the P-2(3/2)-S-2(1/2) transition for elements with Z <= 50. Isotope shifts and nuclear moments can be measured with unprecedented precision, in principle even for only a few stored radioactive species with known nuclear spin. A superior relative line width in the order of 5 center dot 10(-7) may be feasible after laser cooling, and even polarized external beams may be prepared by optical pumping.