Use a zester or grater to remove the lemon zest from one lemon and set aside. Then, juice both lemons, measuring out 1/4 cup of fresh juice.
Chop the basil leaves roughly and add them to a mixing bowl with the lemon zest, juice, and heavy cream.
Use a hand blender or whisk to blend the mixture until the basil is finely chopped and the mixture is combined smoothly. You should see bright green flecks throughout.
Add the sweetened condensed milk and lemon zest to the mixture, folding gently until everything is well incorporated and smooth.
Pour the mixture into a freezer-safe container, smoothing the top with a spatula to ensure even freezing.
Cover the container tightly with a lid or plastic wrap and freeze for at least 4 hours, or until firm and scoopable.
Once frozen, scoop out the lemon basil ice cream with a spoon or scoop and serve immediately, enjoying the vibrant, herbal citrus flavor with a creamy texture.