The outer membrane of Gram-negative bacteria is almost exclusively composed of lipopolysaccharide in its outer leaflet, whereas the inner leaflet contains a mixture of phospholipids. Lipopolysaccharide diffuses at least an order of magnitude slower than phospholipids, which can cause issues for molecular dynamics simulations in terms of adequate sampling. Here, we test a number of simulation protocols for their ability to achieve convergence with reasonable computational effort using the MARTINI coarse-grained force-field. This is tested in the context both of potential of mean force (PMF) calculations for lipid extraction from membranes and of lateral mixing within the membrane phase. We find that decoupling the cations that cross-link the lipopolysaccharide headgroups from the extracted lipid during PMF calculations is the best approach to achieve convergence comparable to that for phospholipid extraction. We also show that lateral lipopolysaccharide mixing/sorting is very slow and not readily addressable even with Hamiltonian replica exchange. We discuss why more sorting may be unrealistic for the short (microseconds) timescales we simulate and provide an outlook for future studies of lipopolysaccharide-containing membranes