An acrylic lamp might look a whole lot like glass from afar, but you shouldn’t clean it in precisely the same way as glass. Conventional household cleansers and even window cleaning chemicals are too harsh for oil. Utilize water and mild liquid dish soap instead.
For a basic cleaning, a damp, lint-free soft cloth is all that’s needed. The cloth has to be wholly non-abrasive to prevent scratching the oil. Use mild dish soap on the damp cloth when the lamp is a bit dustier or dirty, followed by another pass with a fresh damp soft cloth. Turn the cloth over often during cleaning or utilize several to avoid wiping the dirt back onto the lamp. Unplug the lamp and as you work and prevent getting moisture anyplace other than the acrylic portion of the lamp.