Preheat oven to 350F degrees. Coat a standard or jumbo size muffin pan with nonstick cook spray, or line with paper liners.
In a large mixing bowl, whisk together the oil and sugar. Add the eggs, vanilla lemon juice, lemon zest and milk. Stir well to combine.
In a separate bowl, combine the flour, baking powder, baking soda, salt and poppyseeds.
Using a wooden spoon or flexible spatula, fold the dry ingredients into the wet ingredients just until there are no visible streaks of flour. Do not overmix.
Spoon the batter into the muffin tin, 2/3 to 3/4 of the way up. For standard size muffins, bake 25 minutes. For jumbo muffins, bake 30 minutes.
Cool to room temperature in the muffin tin before removing onto a wire rack.
To make the glaze, melt the butter in a microwave safe bowl. Whisk in the remaining ingredients. Drizzle over cooled muffins.