short answer to your question.... LOTS OF LUMENS!!!
If you're doing it at night in a place with low ambient light I'd say that 7K-10K would be adequate. I have done projection during the day but it's tougher.
We built a frame out of lighting pipe and covered it in black velour drape to create an enclosed space for the projectors. Our event was in the early afternoon so we positioned the screen facing east so the sun would be hitting the projection enclosure and not the screen. Then we stacked up 2 Barco R12+ projcectors and converged them to run as one single 20K+ source. It was pretty good but if i did it in daylight again I'd add a 3rd Barco