Cut out rounds of pie crust to fit six 4-inch tart pans. Press into pan, prick all over with a fork and blind bake according to package instructions. Let cool.
For the filling, melt butter in a heat proof bowl set over simmering water. Add sugar, lime juice, lime zest, eggs and salt. Whisk until curd just begins to thicken, about 5 minutes. Stir continuously until curd thickly coats the back of a spoon, about 5 minutes more.
Remove curd from heat and pour through a fine mesh strainer. Let curd cool down, then cover and refrigerate until completely chilled.
To assemble, divide lime curd among tart shells, top with sliced strawberries and serve.