my betta has also gotten a white patch like circle on the LENS of his eye, also my femal bettas, I have heard that this whiteness can be caused by a fungus. A man that raises bettas says that this problem is usually not fatal but it is probably a certain fungus, it can be treated with salt added in the recommended amounts, or by a fungus away type of cure. So far the salt has yet to help the cloudyness of the eye, however I have not tried the fungus away tabs yet. My male bettas eyes seemed to clear up when I placed him in tetracycline, I dont know why b/c the box does not list this as one of the ailments that it treats, by anywho it went away, but when I put him in a tank with filtration he again developed the cloudy hazy lens that has plagued all my bettas.
OR
I think if the fish is malnourished the eye will tend to cloud further into the eye past the lens, but I am not sure of this.