It sounds like your granddaughter has amblyopia in her left eye (this is sometimes called lazy eye). When we are born, our visual system is not yet fully matured. It takes 8-9 years to fully develop. However, in order for your eyes to develop, it has to be able to see. If an eye can see and receive images clearly, it will not develop properly. Things that can block vision (e.g. congenital cataract, scars, crossed eyes) will impair this development. In the case of anisometropia, where one eye is a lot more near-sighted or far-sighted than the other, the brain will use the better eye and shut down the bad eye. Once the child passes the 9th birthdate, there is not much more you can do to strengthen the vision in the eye (not glasses, contacts, surgeries). The key would have been to catch the difference in the prescription while a child is still very young. Glasses to aid the weak eye in the early formative years could greatly improve a lazy eye. Our recommendation is for all children to have an exam by 6 months of age for this reason.
The surgery they spoke to you about in the future is only to correct the focusing, but will not improve her vision beyond what contacts or glasses can do now. The problem with a lazy eye is not the focusing, it is the neurologic "wiring" of the nerves back to the brain that is underdevelop.
Hope this helps.