Preheat the oven to 375^F Pierce the eggfruit in several places with a knife and bake on a baking sheet until soft, about 50 minutes, turning midway through.
Remove from the oven and cool. Cut the eggfruit lengthwise in half. Scoop out as much pulp as possible and coarsely chop.
In a large Dutch oven, heat the oil over a medium-high heat. Add the carrots and saute, stirring, for 5 minutes.
Continue adding ingredientsred capsicum, green capsicum, zucchini, and apple- spacing 3 to 4 minutes apart.
Stir in the eggfruit pulp and half of the garlic, cover, and simmer over low heat for 40 minutes. Add the tomatoes and continue simmering for another hour, stirring from time to time. Off the heat, add the remaining garlic, lemon juice and sugar.
Season with salt and pepper. Transfew the mixture to a bowl, cover, and refrigerate for several hours before serving.