The main reason Lee decided to invade the North was To relieve pressure on Virginia.

By the summer of 1863, the Confederate Army had suffered considerable losses and was under increasing pressure from Union forces in Virginia. Lee was convinced that a successful invasion could redirect the war's focus away from his home state, secure essential supplies, and possibly compel the North to seek a peace settlement. Furthermore, a significant victory in the North could enhance Southern morale and attract foreign recognition for the Confederacy.