Simmer water, milk, butter, sugar, and salt. Stir in flour, cook into a dough, then cool slightly. Beat in eggs one at a time, add vanilla, and pipe into 4-inch strips. Bake at 375°F (190°C) for 25–30 minutes until golden. Cool completely.
Heat milk until steaming. In a separate bowl, whisk sugar, egg yolks, and cornstarch. Slowly add hot milk to temper. Cook until thick, then stir in butter, lemon zest, lemon juice, and vanilla. Chill until set.
Cut éclairs or poke a hole in one end. Pipe in lemon pastry cream until filled.
Whisk powdered sugar, lemon juice, and zest until smooth. Thin with more juice if needed.
Dip tops of éclairs in glaze. Let set before serving.