Preheat oven to 350 degrees Fahrenheit. Line a sheet pan with parchment paper.
Place oil, sugar, egg, lemon zest and lemon juice in to a large bowl and whisk to combine.
Add almond flour, baking powder, and salt, and stir to fully combine. Dough will be wet and sticky.
Scoop the dough into 12 2-Tablespoon sized balls. Bake for 12-14 minutes, or until edges are slightly golden and centers are set.
Let cookies cool for 15 minutes on the pan, then transfer to a cooling rack. Set the rack on top of the parchment-lined baking sheet your cookies just came off of (this will catch all the mess from icing them!).
Stir together all icing ingredients, adding more lemon juice a few drops at a time, if needed, to get a thin, pourable consistency. Use a spoon to scoop about a teaspoon of icing onto each cookie, letting it naturally drip down the sides. Add any remaining icing to any cookies that look like they need it!
Let sit until icing hardens (about 15 minutes) before eating. Store any leftovers in a sealed container at room temperature for up to 3 days.