In a bowl, toss the pineapple chunks with about a 1/2 cup sugar (to taste) and about a 1/4 cup lime juice (or enough to coat all the pieces of pineapple—it's okay it there's some extra juice at the bottom).
Let it sit in the fridge until it's good and cold. Then, puree!
Pour the mixture into an ice cream maker, and freeze according to the manufacturer's instructions. Transfer the sorbet into a freezer-proof bowl and freeze for an hour or two, until solid.
Alternatively (should you not have an ice cream maker), pour the puree it into a large metal bowl and put it in the freezer. After a couple hours, when the mixture is still liquid in the center (but starting to freeze on the edges), whisk it all together. Repeat another hour or so later, then let freeze until solid.
Scoop two or three generous scoops of the pineapple sorbet into a large glass. Pour in some lemon-lime soda water. Or, a bottle of Vanilla Bean DRY soda. That is also tasty. Throw in some rum or something, if you drink alcohol (I do not, so you're on your own with that one).
It's light and frosty and really delicious.
Repeat the last step until all the sorbet is gone. Then start it all over again with mangos. Or honeydew. Or kiwis. Or peaches. Or raspberries. Or strawberries. Or blueberries. Or nectarines. Or any other fruit you can think of.