I thought I would share this strange but beautiful instrument with you, that one of my students brought in to show me. I have never seen or heard of a Lutelele before, but once told one existed I just had to see it. It's quite a strange looking thing, and I must say I thought it looked more like a cross between an old 19th century style Mandolin and a Ukulele, rather than a Lute and a Ukulele. I guess if it had the headstock facing back like we expect to see on a Lute then it would bear more resemblance to a Lute.
That said it was a really fun little thing. I sounded great when I knocked out some Baroque tunes on it. A little bit of John Dowland seemed to really suit it. If I didn't already have too many instruments then I would definitely consider getting one.
I have one that is similar. Here's me playing it: Waltz by Ferdinando Carulli, Low G Classical Ukulele Fingerstyle - YouTube