Cut off the vinyl straps and/or mesh seating along with any other straps from the lawn chairs with scissors. Additionally, untie any cushion straps and pull the cushions off the lawn chairs.
Pull out the strap fasteners hooked into the aluminum frame using needle-nose pliers. Unfasten any screws holding the plastic arms in place with a screw gun, if applicable. Should the arms not come free, pry away from the aluminum frame with claw hammer.
Run a magnet slowly over the entire lawn chair once stripped to find any steel screws, rivets or other hardware attach to the aluminum frame. If any steel is found by a magnetic pull, remove it with pliers, a claw hammer or cut it out with a reciprocating saw.
Throw everything you stripped and/or unfastened from the lawn chair's aluminum frame into a trash bag and dispose of it. Take the lawn chair's clean aluminum frame to a nearby scrap yard or recycling center.