Thaw banana slices and pineapple chunks at room temperature for 5 minutes.
Blend bananas, pineapple, and coconut milk in a food processor until smooth, about 1 minute; add lime juice and kosher salt and process again to mix.
Line an 8x11-inch baking dish with plastic wrap. Pour banana mixture into the baking dish. Freeze until the 'ice cream' is of soft-serve consistency, 30 to 45 minutes.
