Unfortunately there is even more to the story. You then need to compare it to sunlight, which is on the order of 100,000 lux. Which will make the problem seem hopeless. But you are not illuminating a spot on the ground with your display and trying to get that spot to compete with sunlight. You are trying to create contrast with the sunlight reflected from the surround of your display. So, except for pathological cases such as looking at a west facing display at sunset the sun is not normal to the surface and illumination efficiency drops accordingly. In the pathological case the sun is going through a much longer atmospheric path and drops intensity a lot. Add a little shade over the display and you can knock an order of magnitude off the solar intensity, maybe more. You need to figure out the amount of light reflect that goes in the direction of the viewer. And then compare that to the amount from the display that goes that direction.
All a lot of computation, with many assumptions to be made.
You may find it easier and far more informative to set up a simple outdoor test with a few LEDs with known specs and then just do relative calculations. Important parameters to know about the LEDs are rated brightness, beam angle in both horizonatal and vertical directions, and how much of the visual field they fill. Comparisons of the results will be much easier if the LED or LED array fills a resolution element of the eye (roughly 0.3 mR).