I’m so pleased you enjoyed it. Love that cake. Keeps really well, too.
As for the oil, I use it whenever I want to amp up lemon flavor in a batter. Mostly cakes. (I admit I haven’t used it for non-cake applications like pies or crumbles, and have never used it in a non-sweet context.) So if a recipe calls for lemon juice and/or zest, sometimes I supplement with a very small amount of oil to get it more lemony. If I am baking something and find I don’t have enough lemons for the recipe, I use the oil to bridge the gap. Since the oil is so strong, you only have to use a little, which means you don’t have to guess/figure out how to adjust the other liquids in a recipe. There’s no impact on the proportion of butter to sugar to flour, and no textural changes (unlike adding, say, lemon zest.) And if I have a batter that’s a different flavor altogether, like almond, I simply leave out the almond extract and add a small amount of the lemon oil, and that’s it- no other mental gymnastics required.
I have a small bottle of lemon oil, and I also at one point bought a “variety” sampler of lemon, orange and lime oils made by the same company. I love them all. I keep them all in the fridge once they’ve been opened.