Preheat the oven to 375º.
Before juicing the lemon, remove the zest with a microplane and set aside. Then squeeze the juice from the lemon—you will need 1 Tablespoon of lemon juice and can discard the rest.
Mix the non dairy milk with the lemon juice.
Add the other wet ingredients (applesauce, oil, vanilla, lemon extract, lemon zest, and sugar) and set aside.
Grate the carrots (I use my food processor fitted with the grater dis)c.
Mix the dry ingredients (flour, baking soda, baking powder, salt) in a large bowl.
Pour the wet over dry and mix together. This will be a fairly stiff batter.
Add the grated carrots and mix until fully incorporated.
Grease a bundt pan with non dairy butter. I like to put a pat of butter on a paper towel and wipe it around the pan. Be sure to get in all of the nooks of the pan.
Put turbinado sugar in the greased bundt pan and gently shake the pan around, coating it with the sugar. (this is optional, but oh so yummy! It gives the cake a slightly sweet and crunchy crust.)
Pour the batter into the prepared bundt pan.
Bake for 45-50 minutes, or until it is golden brown and a toothpick comes out clean.
Allow to cool for a few minutes before inverting it onto a cooling rack and releasing the cake. Then allow to cool completely on the cooling rack before glazing.