Everyday renovation debris is fine. The restrictions come from the City's own list and from Ohio rules.
Lancaster publishes a detailed unacceptable waste list. It covers hazardous waste, explosive materials, liquid waste including motor oil, asbestos, whole and shredded tires, lead acid batteries, drums and barrels, motor vehicles and major parts, equipment and machinery, appliances still holding refrigerant, ashes of any kind, and medical or radioactive waste. The City counts paint, gasoline, lacquer thinner, propane tanks, and the empty containers they came in as hazardous.
The transfer station adds its own refusals on top. Shingles, concrete, block, brick, dirt, gravel, mulch, lumber longer than four feet, liquids, metal vehicle parts, and metal pipes are all turned away there.
Statewide, Ohio has barred lead acid batteries from landfills since 2008, and a landfill must refuse a load of yard waste that has been separated out from other trash.
Yard waste also cannot be mixed in with ordinary waste in the same container under City rules. Ask your account manager where any of these belong before loading day.