Ordinary building and household debris is accepted. The exclusions come from Virginia's solid waste rules, which the regional authority applies at the scale, and the city will not collect anything the landfill would refuse.
Out entirely: free liquids, regulated hazardous waste, material containing dioxins or PCBs, untreated sewage sludge and combustion ash, contaminated soil, asbestos, regulated infectious waste, and large animal carcasses. Pesticide containers have to be triple rinsed and crushed, and drums have to be empty, cleaned, and cut open at both ends.
Waste oil is banned too, with one exception for residents on the regional household hazardous waste collection days. Those same days are the route for paint, antifreeze, brake fluid, solvents, pool chemicals, herbicides, and batteries, none of which belong in a container.
One Lynchburg-specific point catches contractors out. The regional authority treats construction and demolition debris as special waste and clears it case by case before it is accepted. That approval needs to be in place before the load reaches the scale, and your account manager handles it with the authority so your haul is not turned around.