We use Lunar Orbiter Laser Altimeter topography data to revisit the depth (d)-diameter (D), and central peak height (hcp)-diameter relationships for fresh complex lunar craters. We assembled a data set of young craters with D ≥ 15 km and ensured the craters were unmodified and fresh using Lunar Reconnaissance Orbiter Wide-Angle Camera images. We used Lunar Orbiter Laser Altimeter gridded data to determine the rim-to-floor crater depths, as well as the height of the central peak above the crater floor. We established power-law d-D and hcp-D relationships for complex craters on mare and highlands terrain. Our results indicate that craters on highland terrain are, on average, deeper and have higher central peaks than craters on mare terrain. Furthermore, we find that the crater depths for both mare and highlands craters are significantly deeper than previously reported. This likely reflects the inclusion of transitional craters and/or older and/or modified craters in previous work, as well as the limitations of the stereophotogrammetric and shadow-length data sets used in those studies. There is substantial variability in the depths and the central peak heights for craters in a given diameter range. We suggest that the differences in mean d and hcp as a function of crater diameter for highlands and mare craters result from differences in bulk physical properties of the terrain types, whereas the variability in d and hcp at a given diameter may reflect variations in impactor properties and impact parameters.