Preheat your oven to 325°F. Grease and line an 8"x8" (or 9"x9") baking pan with parchment paper.
In the bowl of a stand mixer (or a large bowl with a hand mixer), use the paddle attachment to cream the sugar and dairy-free butter together for 3-4 minutes until light and fluffy. Stop to scrape down the sides as needed.
Crack the eggs into the bowl one at a time and mix after each addition. Add the ripe bananas and mix, starting on low and increasing to medium speed, until they are fully broken down into tiny pieces within the wet batter. Mix in the lemon juice, vanilla extract, and half of the dairy-free milk.
In a separate small bowl, mix together the gluten-free flour, baking soda, baking powder, cinnamon, and salt. Pour half into the batter and mix gently to incorporate. Add the remaining dairy-free milk, mix, and add the remaining flour mixture. Mix on low speed just until everything is combined. Use a rubber spatula to scrape the bottom and sides of the bowl, ensuring no dry spots.
Pour the batter into the prepared baking pan. If using an 8"x8" pan, bake for approximately 38-40 minutes until a toothpick comes out clean. If using a 9"x9" pan, begin to check the cake with a toothpick around 30 minutes and remove when the toothpick comes out clean. Allow the cake to cool in the pan for at least 30 minutes, or until it is cool enough for you to lift it out of the pan with the parchment paper. Place on a wire rack to cool completely, about 2 hours or overnight.