The measurement accuracies of three-frequency resonance fluorescence Doppler lidars are limited by photon noise and uncertainties in the laser frequency and line width. We analyze the performance of Na, Fe, and He lidars using a new technique, which incorporates precise information about the absorption spectrum of the species and the pulse spectrum of the lasers. We derive the measurement errors associated with photon noise, laser frequency errors, and laser line width errors. Optimizing the lidar design, based upon the measurement requirements, can improve system performance by reducing the required integration times, enabling measurements to be made in less time or at higher altitudes where the densities and signal levels are smaller. The optimum frequency shift for observing heat and constituent transport velocities is 689 MHz (580 MHz) at night (day) for Na lidars and 774 MHz (597 MHz) for Fe lidars. The optimum frequency shift for observing winds, temperature, and He densities is 3.66 GHz (3.16 GHz) at night (day) for He lidars.