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Preheat the oven to 350 degrees F. Line a loaf pan with parchment paper, leaving an overhang off both sides, and grease the pan well.
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In a large mixing bowl, cream together the butter, sugar, and lemon zest until light and fluffy, using either a stand mixer or hand mixer.
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Add the lemon juice and eggs and continue mixing, until light and fluffy again.
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In a separate bowl, mix together the flour, baking powder, and salt.
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Pour the dry ingredients into the wet ingredients, and add the oat milk as well. Stir until just combined.
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Pour the batter into the loaf pan. Bake at 350 degrees F for 45 to 55 minutes, or until a toothpick pulls out clean from the center.
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Let the cake cool in the pan for 10 minutes, then use the parchment paper overhang to lift the cake and place on a metal cooling rack. Let cool completely.
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While the cake is cooling, prepare the glaze: Mix the powdered sugar, lemon juice, and oat milk in a small mixing bowl.
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When the cake is cool, pour the glaze over the top and let it spread over the cake. Wait a few minutes for the glaze to set, then dig in and enjoy.