One direction to look in might be the various GIS systems that exist to forecast the amount of light that will reach photovoltaic (solar panel) installations. I don't know about the US, but I would be very surprised if there isn't one - try googling for "PV GIS" or similar.
Now, that will give you insolation (illuminance) in W/m2. It may be further broken down into direct and indirect insolation (that's direct sunlight and diffuse light from the sky or clouds), or it may be a single global figure.
Since you're after the information in lux rather than W/m2, you'll need to convert it. This will necessarily be an approximate process, but so long as you don't need very high accuracy it should be quite doable. Lux is at base a measurement of power density, just like W/m2, but it's modified by a frequency-dependent function that represents the sensitivity of human vision. So you'll need to assume a spectrum for the sunlight, and then apply the conversion curve (which is an international standard, and hopefully available on the internet).