Remove cream cheese, eggs, and sour cream from refrigerator 1-2 hours before starting. Preheat oven to 325°F (165°C) with rack in center. Grease 9-inch springform pan, wrap outside tightly in 2-3 layers of heavy-duty foil, and boil water for water bath.
Crush graham crackers into fine crumbs. Mix crumbs with ¼ cup sugar, then stir in melted butter until mixture resembles wet sand. Press firmly into bottom and about 1 inch up sides of pan. Bake at 325°F for 8-10 minutes until toasty and set. Cool slightly.
Beat softened cream cheese on medium-high for 2-3 minutes until smooth. Add sugar and beat 2 more minutes. Add sour cream, lime juice, lime zest, and vanilla; beat 1 minute. Add eggs one at a time on low speed, mixing just until blended. Fold gently with spatula.
Pour filling over warm crust and smooth top. Tap pan on counter to release air bubbles. Place foil-wrapped pan in roasting pan on oven rack. Pour hot water into roasting pan until 1 inch up sides of springform pan. Bake at 325°F for 65-75 minutes until edges are set and center has gentle jiggle.
Turn off oven, crack door open 1 inch, and leave cheesecake inside for 1 hour. Remove from water bath and peel off foil. Run thin knife around edge to loosen. Cool completely on wire rack for 1-2 hours. Cover and refrigerate at least 6 hours, preferably overnight.
Just before serving, beat cold heavy cream until soft peaks form. Add powdered sugar and vanilla, beat until stiff peaks form. Release springform ring, transfer cheesecake to serving plate. Top with whipped cream, extra lime zest, and lime slices. Serve immediately.