Unless they've changed the definition, all lazy eye (amblyopia) is entirely neurological, since amblyopia refers to brain's ignoring the signal coming from one of the eyes, leading to the atrophy of the optic nerve and/or vision centers of the brain.
Many physical conditions can *cause* amblyopia (strabismus being the best-known), and some of them can be corrected surgically, but the only way to correct amblyopia itself is with vision therapy exercises that force the person to rely only on the "lazy" eye. These exercises can be helpful at any age, but only up to about age 6 can the vision be made completely normal again.
My lazy eye was detected too late to cure it (even though I was only 4, but it was too late anyway) and to this day (25 years later) my best corrected [that is, with the most accurate contacts/glasses prescription they can make] vision in that eye is 20/70 because what I see out of that eye quite simply doesn't make sense. Like if I cover my good eye and try to read, I can't just see a word and read it, I have to think about the shape of each letter and then put the letters together like I did when I was a small child, and I get a headache very quickly from doing so.
My sister also had one but they caught it at age 2½ and corrected it, and she's got great vision today, although she needs glasses for reading.