Certified GKH Gardening Expert
I'm sorry, there is no way to diagnose deficiencies and issues while under colored LED. It will not allow me to see coloration of the problem, or any details when under this lighting.
Most commonly, when grown indoors, beans will suffer from overwatering, and too much nitrogen in soil.
Using LED further leads me to believe overwatering.
It could be the LED itself, though, if it only has red and blue diodes. I don't recommend LED panels with less than 9 bands of light spectrum. Really, I would go a step further with an 11 band that includes ultraviolet and infrared, since these are the spectra of light that kill infections.
For this reason, I do not recommend LED unless they are a high end panel. The ones offered at a budget (I have yet to find even a decent unit for under the $500 mark) lack much of the important things needed for plants, unfortunately.
I think that if you changed over to Ceramic Metal Halide, that most of your problems will subside. They help with overwatering, since they provide heat to evaporate some of that water, and moderate amounts of Ultraviolet and infrared. It is a 315 watt unit that will light a 4x4 area very efficiently. Anything you can fit under a 4x4 area of light will flourish as if it were under the sun.
One more piece of information... This is the part that isn't so easy to hear. Beans aren't the easiest to grow indoors. They are susceptible to many diseases, and bug problems are amplified 10 fold indoors. Feeding them is quite annoying because you must use a feed with postassium and phosphorus but NO nitrogen. They will fix that from the atmosphere.
I do beans indoors, myself, but even after doing this for more than a decade... I run into my fair share of problems with them still. Trial and error will be the way to learn. That, and get a light that allows you to see proper color when inspecting at the very least.
Here is an article that will help you, further, with the care of beans: