"Three factors will decide the number of lumens required for a room: distance between the farthest viewer and the screen; the amount of ambient light in the room while presenting; and the "gain" reading of the projection screen. "
Here's the article and it includes a method to calculate what you need:
The most important criteria is the size of the screen. What is important is the area. You have a fixed amount of light coming out of the projector and you will distribute this amount over the area of the screen. If your light is correct for a 3 x 4 screen then a 6 x 8 screen will require 4 times as many lumens.
The next factor is the amount of light in the room (ambient light) this will have the effect of washing out the image. With a dark room you can get by with less.
I run a theatre with a 15 x 20 foot screen. My projector, an EIKI, has four seperate lamps. We usually run on two for our daily films, a rating of 5000 lumens, When we do presentations with lights on for the presentors we will run all four lamps for a rating of 10,000 lumens. We will also run four lamps whenever we show a wide screen presentation, because we open our side masking to reveal the larger screen area. Bigger area needs more light.
The contrast ratio of the projector is an important factor. With a low contrast ratio it will seem dimmer for the same brightness.
The distance from the projector to the screen has little effect on the brightness, except that long throw lenses are usually less efficient than normal lenses. Less light will be transmitted through those lenses.
I know that I haven't given you a straight answer but those are the factors that should be considered.
i have installed several 80'+ screen with film and Digital projection .. The screen will be ussually a Harkness or a MDI or a maybe a Stewart .. The effective gain will .9 or less , but lets say .9 (in some cases (and what I spec) it will be a higher gain screen if used ONLY for DP... This is often not the case though ..
This will be a ~3000 sq. ft screen , you will need 36,600 lm to meet SMPTE specs ..
This means a dual or triple stack 12-18,000lm projector with the 2k DLP chips ..
OR 3 x 12,000 - 18,000lm with edge blending ..
This is really on the low side for some screens ... I would use a Digital projection or Christie DLP head with a 8k-12k (thats lamp power - not lm) lamp house, heat shield and water cooling ..
i can give you exact set up and specs and custom design the lens and whole theater for you -- but people pay me money to do that .... but this will get you going ... ..