Pour the olive oil into a large pot and set over medium-high heat. Add the onion and sauté for several minutes until tender. Add the garlic and ginger, sauté another minute or so.
Add the broth, coconut milk, and curry paste and stir to blend. Stir in the lentils, brown sugar, and fish sauce and stir well.
Simmer for 5 minutes and add the carrots and zucchini. Cook another 8 to 10 minutes until the lentils are tender and the soup has thickened. Add the juice of the lime and stir well. If the soup is too thick for your liking, add a little water. Taste and add salt, if desired.
Serve in bowls with cilantro scattered over the top to garnish.