He may very well have 'poop stuck', an obstruction, a bloat or infection in the gut may cause symptoms like this. All of these can be fatal, especially in young lambs.
I still think getting a poo sample to the vet may help you, as it does not sound like normal healthy defecation at all.
Then it may be the case that the vet recommends feeding electrolyte solution instead of milk for a period. After that, it may be time to wean, providing it is eating enough hard feed to compensate for losing the nutrition in the milk.