The site and bond percolation problems are conventionally studied on (hyper)cubic lattices which afford straightforward numerical treatments. The recent implementation of efficient simulation algorithms for high-dimensional systems now also facilitates the study of D_n root lattices in n dimension as well as E_8-related lattices. Here we consider the percolation problem on D_n for n=3 to 13 and on E_8 relatives for n=6 to 9. Precise estimates for both site and bond percolation thresholds obtained from invasion percolation simulations are compared with dimensional series expansion based on lattice animal enumeration for D_n lattices. As expected the bond percolation threshold rapidly approaches the Bethe lattice limit as n increases for these high-connectivity lattices. Corrections however exhibit clear yet unexplained trends. Interestingly the finite-size scaling exponent for invasion percolation is found to be lattice and percolation-type specific.
