Heat oil to 375 F (190 C). You can use a deep fryer, or a heavy pan. If not using a deep fryer, use a deep, heavy pot, filled to at least 3" deep.
Whisk together milk, lemon juice, egg, vegetable oil, and vanilla until well combined and smooth, set aside.
In a large mixing bowl, combine remaining (dry) ingredients. Add wet ingredients to dry, stirring with a whisk until well incorporated. Allow to sit for 10 minutes.
Using two teaspoons, scoop out approximately 1" balls of dough, carefully dropping them into the hot oil. (Do NOT splash yourself!).*
Cook for about 3 minutes, flip doughnut holes onto their other sides, cook for another 2-3 minutes.
Cook a few donuts at a time, being careful to not over crowd your fryer / pot.
When doughnut holes are cooked, use a (metal!) slotted spoon to transfer them from the oil, to a pan lined with paper towels. Once all donuts are cooked, allow to cool for a few minutes.