Not sure it qualifies as recyclable. A vet will dispose of the carcass properly for a fee or the local council will help but if you want to save money perhaps you could cremate it on the patio?
Just leave it on the patio and forget about it. Foxes and cats will come and do the rest free of charge, you'll have done your bit for nature, and your dog will remain in the circle of life.
When did Lucky... there's no easy way to say this - pass away? Obviously I take it that he (I don't know how I know Lucky was male, but I'm picturing a dog with a cock) was a Brighton fan (probably had a BHA dog bowl - oh god it's breakfast time, and I bet he loved breakfast - right now he'd be wagging scruffy little tail - sorry, I digress), so it would be nice if we could put the date on our calender, and remember him each year.