Thaw the phyllo in the fridge overnight. Preheat the oven to 350°F and butter a 9x13-inch baking dish.
Working with two sheets at a time, loosely ruffle the phyllo into folds about 1 inch thick and stand them up in the dish, folds facing up, until the dish is loosely filled.
Bake for 10 minutes. Remove, drizzle the melted butter evenly over the phyllo, and bake 10 more minutes.
Meanwhile, whisk the milk, eggs, sugar, vanilla, and almond extract for the custard.
Pour the custard evenly over the baked phyllo and tuck the sliced strawberries between the folds. Bake 30 to 40 minutes, until golden and set.
Make the syrup: simmer the sugar, water, and lemon juice for about 10 minutes, until lightly thickened.
Pour the warm syrup evenly over the pie. Let cool to room temperature, then slice and serve.
Notes
Best made a day ahead so the custard sets. Store covered in the fridge up to 3 days. Add the strawberries in the final bake so they stay juicy.