Reddit mentions of Miuzei 20KG Digital RC Servo Motor High Torque Servo Metal Gear Waterproof Servo for R/C Car Robot, DS3218MG Control Angle 270°

A simple servo would do it; most have a movement range of about 120 degrees. Some like this have a much larger movement range https://www.amazon.com/Miuzei-Torque-Digital-Waterproof-Control/dp/B07HNTKSZT/ref=sr_1_25_sspa?keywords=servo&qid=1557374596&s=electronics&sr=1-25-spons&psc=1 those are cheap no-name servos but they have performed surprisingly well for me; if you want to get something expensive then HiTec is good. You can control it directly from the Pi if you want to, or you can use a dedicated controller board like a https://www.amazon.com/SunFounder-PCA9685-Channel-Arduino-Raspberry/dp/B014KTSMLA/ref=sr_1_5?keywords=servo&qid=1557374551&s=electronics&sr=1-5 which will sit between the servo and the Pi. The only concern is that the servo may need a maximum of 2 amps when moving, so you just need to ensure that the power supply for the system is sufficient - so a connection to a decent USB wall charger will be good, but a common PC USB port wouldn't provide enough power.

For the actual setup, consider where you actually mount the motor. You may not be able to attach it directly to the lampshade, but you may be mounting it to the table or base of the lamp and connecting it to the lampshade through a small rod. It's just one of the "oh, of course" things you'll run into when trying to bring the parts together. The pivot point for most lampshades is on the bulb, but you don't want to attach the servo to the bulb.