Add the lentils to a saucepan, along with the vegetable stock, garlic powder, and smoked paprika. Bring to a simmer, and cook until the lentils are very soft and have cooked right down into the liquid. Allow the mixture to thicken a little - it should still be fairly wet, but with no excess liquid (mine took about 20 minutes in total).
Meanwhile, grate the courgette (zucchini), and thinly slice the potatoes.
When the lentils are cooked, add the grated courgette, and mix to combine.
Add half of the lentils to a baking dish (mine measured around 10 x 10 inches), and top with half of the sliced potatoes (in a single layer, if possible - it's okay if you need to overlap them a bit). Drizzle over half of the goat's cream, and top with half of the chopped chives and half of the grated goat's cheese. Repeat the layers a second time to use up the remaining ingredients.
Cover the dish loosely with foil, and bake at 190°C (Gas Mark 5 / 375°F) for around 1 hour, until the potatoes are fairly soft. Remove the foil, and return to the oven for a further 25 minutes, or until the cheese has crisped up to your liking. Allow to sit for a few minutes before cutting to allow the lentil gratin to firm up a little.