Ever since I got my kid the Lego Robot Inventors 51515 kit, I have been looking for a good way to store the pieces and I think I have finally found the solution thanks to www.RoboticsLearning.com!
On that website, I found a link to a storage organizer system sold at Harbor Freight: Storehouse Toolbox organizer with 4 drawers. If you dont have a harbor freight near you, I think these from Amazon are similar organizer systems:
Here are some images of my organized 51515 kit:
https://photos.app.goo.gl/bxrgZ6fAAvpn5eyG7
Here is where you can buy the labels ($10 for the PDF) and find more information on RoboticsLearning.com: LEGO Robot Inventor Set Case Label PDF Files (roboticslearning.com)