I don't think it's a lost cause - the thing about pretty much ANY italian car of any value is that they require a fair amount of money throwing at them to keep them at the top of their game. A lot of people do this because they love the car/brand, others do it because they want to be different and put up with the costs. If you don't fall into that catagory it'll be best to get rid of it before it becomes hard to sell, so that someone else who loves it enough or has enough cash can lavish it as it needs to be lavished.
It's probably not the easiest thing to find, but if you phone Omicron (+44 1508 570351) they might be able to either find a replacement gearbox for not too silly money, recommend a fix, or something like that. I wouldn't want to remove, strip, rebuild and refit a delta gearbox if I could avoid it, but if it's not 4WD it won't be too difficult. Oh, at Omicron it'll be Andrew you need to speak to, since Elizabeth and Martin don't really know their modern Lancia's (in which the Delta falls).