In large bowl, combine sugars with peaches. Mix gently. Cover and let stand for 1 hour.
Line pie pan with bottom crust. Drain peaches, reserving juice.
In small saucepan, combine cornstarch, cinnamon, and salt. Gradually stir in juice. Cook over low heat for 2 minutes, stirring constantly until thickened. Remove from heat. Stir in lemon juice and butter.
Gently fold in peaches. Pour into bottom crust.
Cut remaining crust into lattice strips and make into a lattice top crust. (Or you can leave whole, if you wish.)
Cover edges loosely with foil and bake at 400 degrees for 45 minutes or until crust is golden and filling begins to bubble. Cool on wire rack.