. I'll take a stab at this.
I don't think you're DQ based on your visual acuity.
The regs state , "...for entrance into USMA or ROTC, distant visual acuity that does not correct to 20/20 in one eye and 20/40 in the other does not meet the standard." You say you are corrected to 20/20 in one eye and 20/40 in the other, so you're good.
You also say you have lazy eye. The correct medical term for lazy eye is amblyopia which is basically the eye not having a visual acuity of 20/20. Some people use the term lazy eye for a condition called strabismus which is technically incorrect.
The key is what's causing the amblyopia? The most common cause of amblyopia is strabismus which is basically your eyes aren't looking in exactly the same direction when you're looking at an object.
One (or maybe both) of your eyes probably deviates and therefore misaligned. There are standards for how much the eye can deviate. An exotropia is one where one or both eyes deviate outward. Esotropia is inward and hypertropia is one where one eye is higher than the other.
The reg also states, " For entrance into the USMA or ROTC programs, the following conditions are also disqualifying: esotropia of over 15 prism diopters; exotropia of over 10 prism diopters; hypertropia of over 5 prism diopters."
As a side note, the DoDI that DODMERB uses says esotropia, exotropia, and hypertropia are DQ. However, there is an additional sentence..." For entrance into Service academies and officer programs, the individual Military Services may set additional requirements."
So your DQ may actually be some type of tropia and the deviation of one (or both) of your eye(s) is beyond the standards for the Army.