This work derives the Cramer-Rao lower bound (CRLB) for an acoustic target and sensor localization system in which the noise characteristics may depend on the location of the source. The system itself has been previously examined, but without deriving the CRLB and showing the statistical efficiency of the estimator used. Three different versions of the CRLB are derived, one in which direction of arrival (DOA) and (shockwave based) range measurements are available (“local estimate” based CRLB), one in which two types of DOA measurements and the time difference between them is available (“native measurement” based CRLB), and one in which only DOA measurements (bearing) are available (“bearings-only” CRLB). In each case, the estimator is found to be statistically efficient; but, depending on the sensor-target geometry, the range measurements may or may not significantly contribute to the accuracy of target localization. Additionally, the native measurements are found to result in superior localization when compared to the use of the range estimates.