How many lumens you need for projection mapping comes down to two things: how much light is already on the surface, and how big the surface is. A projector cannot make anything darker, it can only add light, so every lumen of ambient light on the wall is a lumen your projector has to out-shout. That is why a 1,500 lumen projector in a blacked-out room can look better than a 4,000 lumen one on a porch under a streetlight.
Here are the numbers that actually hold up, then the reasons behind them.