In a large bowl, whisk together the sweetened condensed milk, heavy cream, lime juice, and lime zest until smooth and fully blended.
Pour the base into a 1½-quart electric ice cream maker and churn until thick and the texture of soft serve, 25 to 30 minutes.
Add the chopped graham crackers and churn or stir just until they're evenly distributed.
Transfer to a freezer-safe container and freeze until firm enough to scoop, 4 to 6 hours.
Notes
Freeze the ice cream maker bowl solid: Put the bowl in the freezer for at least 24 hours before you churn, until you can shake it and hear no liquid sloshing inside. A bowl that isn't frozen all the way through can't freeze the base as it churns.Zest the lime before you juice it: Grate the zest off the whole lime first, since it's hard to zest a lime once it's been cut and squeezed. Take only the green outer layer and stop at the white pith, which tastes bitter.Use full-fat dairy: Heavy cream is what keeps this smooth and scoopable, so don't swap in a lower-fat milk or cream, which freeze harder and icier.Store it airtight with wrap on the surface: Press a piece of plastic wrap right against the top of the ice cream before you cover it. That keeps air off the surface so ice crystals and freezer burn don't form.