Hi John,
Unfortunately, you cant use lumens per square foot as a criteria for good lighting. If you've read something that suggests a certain lumens per square foot as a good amount of light, you can consider that source as non-credible because they dont know what they're talking about. Also, there is no "rule of thumb" for lumens per square foot.
I'll try to demonstrate... imagine a room that's 10' x 10' where you have a 1000 lumen light source. You would think that you have 1000 lumens per 100 square feet, or 10 lumens per square foot. Now...raise the ceiling up to 20'. You still have 10 lumens per square feet, but the light source is much further away. Now, raise the ceiling to 50'. Do you still have the same amount of light? No.
Also extremely important is the source of the light. Is it a light bulb that shines in 360 degrees, or is it a spot light that only shines in one direction? Where are your lumens going? Are the walls a shiny white surface or a rough cinder block surface. Are your lumens reflecting off the walls or not?
All of these things and many many many others determine how much "light" you will have in your space.
The correct thing to do is to get a lighting layout for your space. For this, you'll need to supply the dimensions, HxWxL, the wall, floor, and ceiling surface materials, and the expected use of your space (which you've done). Get this info to someone that can do a layout for you and you'll have a perfect answer.
If you look at the stickies at the top of the lighting and electrical section of the forum, there is a lighting layout thread. There may already be a layout there that aligns with your dimensions. It's might already be done for you!
Sorry to be a downer on your request, but you'll be much better off if you get a layout done.
Good luck,
CD