Lexan is a thermoplastic called polycarbonate. The practice of gluing plastics together is known as "plastic welding." The glue of choice for Lexan is the chemical solvent methylene choride (also called dichloromethane). Solvents like methylene chloride dissolve the polymers present in polycarbonate, allowing the two pieces of plastic to melt into one piece. The "welded" joint is therefore very strong because it is technically one piece of plastic.
Identify the areas on each piece of Lexan that you wish to glue. Rough these areas with your sandpaper--this ensures a strong bond after gluing.
Apply the polycarbonate solvent, which contains methylene chloride, to one piece of Lexan.
Press the two pieces of Lexan together and hold them in place. Use clamps or a vice if possible for a strong, stable bond
Wait 20 to 30 minutes before handling your Lexan. Most of the solvent will have evaporated after this time; however, the bond will be at its strongest after 24 hours.
Use plenty of solvent when gluing your Lexan. It is better to over-apply rather than under-apply the solvent.
Methylene chloride is a moderately dangerous chemical. Use this solvent in an area with adequate ventilation and avoid contact with skin.