Can wearing an eye patch, closing one eye, improve vision and minor eye lag/lazy eye in other eye? How much training would it take to improve

Possibly. If you had patching when you were an infant and a young child, then your eyes (each alone) may have reached their best potential vision by age eight. The vision can then drop in one of the eyes and be brought up to its best 8 year old level when you are older. If the vision was poor by age eight, then you are out of luck.