Burn off the spines and tiny needles (called glochids) using tongs and a grill or gas burner. Set aside to cool.
Cover anything likely to stain. Wearing gloves, peel the fruits, discarding the tough ends and the peel and spines. You can compost this.
Run the fruits through a food processor or juicer, then a fine mesh sieve to remove the seeds. You should have 2 1/2 C. (600 ml) of thick juice.
Add the agave syrup and the lemon juice, tasting as you go. You might not need as much agave if your fruits are really ripe. Hank recommended using citric acid (Fruit Fresh) but I think I like the taste of the lemon juice better. The tartness is needed to balance the sweetness of the fruit, which is an excellent source of Vitamin C.
Put the mixture in a large shallow baking dish, then into the freezer. Remove every 30-45 minutes and rake it with a fork to form icy, slushy crystals.