Get the butter and cream cheese out of the refrigerator and leave at room temperature until softened.
Capture the flavor of the lime.
I used a microplane to zest it, and juiced it by reaming it with a tablespoon over a strainer.
Put the butter and cream cheese in the bowl of your stand mixer with the paddle attachment.
Start the mixer on low speed until it breaks up the big lumps, and then increase the speed gradually to medium until it smooths out the smaller lumps. Stop to clear the paddle and scrape the sides and bottom of the bowl several times with your flexible spatula.
Add the lime juice and zest and the vanilla (overpour a little) and run the mixer until it blends in.
Add the powdered sugar one-third at a time. With each addition, run the mixer slowly at first and speed it up until all the sugar is blended. Stop occasionally to clear the paddle and scrape the bowl.
At the end, run the mixer on a higher speed (I use 6) for a minute or two until it has no more lumps and a satiny texture.
Remove the paddle and free the bowl. Use your flexible spatula to scrape all the frosting off the sides and bottom of the bowl, and then fold and blend until all the streaks are gone.