Crumble cookies into a food processor and pulse until finely ground. In a medium bowl, toss 2 tbsp. lemon zest with 1 1/2 tbsp. sugar.
Add cookie crumbs and mix well. Butter sides of an 8-in. pan with removable rim and press cookie mixture into bottom; bake 15 minutes.
Remove from oven and let cool in pan.
Lower temperature to 27
In standing mixer fitted with paddle attachment, beat goat cheese and cream cheese until light and fluffy.
Add remaining lemon zest, 1 tbsp. lemon juice, the orange zest, 3/4 cup sugar, the sour cream, and the vanilla; beat well. Scrape bowl and add eggs; beat well.
Pour batter onto crust and bake about 1 hour, or until set on the sides but still quite jiggly in the center and only slightly sticky. Turn oven off, crack oven door, and let cake cool in oven 2 hours.
Remove and let cool completely; then chill, covered, at least 2 hours and up to overnight.
Run a thin knife between cake and rim of pan and remove rim. Thinly slice strawberries, then toss with remaining 2 1/2 tbsp. sugar and lemon juice. Arrange on cake.
