Sift together flour and salt into a food processor. Add the lard and butter and pulse until the size of small peas. Gradually add ice water, until dough comes together in a ball. Shape into 2 balls, wrap in plastic, and refrigerate for at least one hour.
Preheat oven to 450 degrees. Roll out 1 pastry ball and line the pie pan with it. Pour filling into pie dish and dot with butter. Roll out remaining pastry and fit to top of pie. Pinch the edges closed. Slice three holes down the center to allow steam to escape.
Fit aluminum foil around the edges to prevent burning. Bake for 20 minutes, reduce heat to 375 and bake for 20 minutes, remove foil and bake another 20 minutes. Remove and let cool.
For the filling
Combine apples, sugar, thyme, rosemary, salt, corn starch, lime juice and lime zest in a large bowl and set aside for 1-2 hours.