If you haven’t heard of a harp-lute, that’s because it was invented by Edward Light in 1795 and was briefly a sort of fad among young ladies in the Regency. Regency ladies liked it because they could accompany their singing with it. Once the piano replaced it as the instrument of choice for that, the harp-lute fell out of favor. There is still interest in it as part of the development of the guitar, though, and you can find a host of images here. Here’s an image of one in the Metropolitan Museum.