Combine peaches, 2 tablespoons sugar, and lemon juice in heavy large saucepan. Cover and cook over medium-high heat until sugar dissolves and peaches are juicy, stirring occasionally, about 5 minutes.
Uncover and cook until peaches are tender and juices thicken, about 5 minutes. Cool compote.
Using electric mixer on low speed or in the bowl of a stand mixer, beat cream cheese until fluffy. Gradually add 1 1/4 cups sugar and beat until smooth. Beat in eggs 1 at a time. Mix in sour cream and vanilla.
Spoon half of cheesecake batter (about 3 cups) into crust. Spoon peach compote over by tablespoonfuls, spacing apart.
Top with remaining cheesecake mixture.
Place large piece of foil on oven rack. Place pan with cheesecake on foil. Bake until puffed, set in center, and beginning to brown, 60 to 75 minutes, until brown on top and center is set. Low and slow is what you want.
Place hot cheesecake on cooling rack; cool 5 minutes. Run small sharp knife around edge of cheesecake to loosen from pan. Place cheesecake, uncovered, on rack in refrigerator and chill overnight. (Can make up to 2 days ahead. Cover and keep chilled.)