The problem is the nutritional needs. Goats need a lot more copper than sheep. So you would have to figure out how to get the proper nutrition to the proper animal.
I have 2 lambs (9 month old wethers) and 1 female goat. They get along fine. They love to play tag. Barbie (the goat) has been trying to teach the boys to head butt. They couldn't seem to get it because goats and sheep butt differently, so now they just gently touch heads. I have been amazed at how well the 3 of them get along. I thought Barbie would be lonely for a goat friend since she came into the group as an adult, but she seems content as long as the boys don't get too far away.
yes, it would work. You can't put any goat feed out for the lamb to eat. Has to always say for sheep on it. If you are planning on breeding your goat, she may need to be trained to eat some goat feed away from the lamb, so she has access to more copper. Since goats that are in production do have a fairly high copper requirement. Goats can very easily be trained to lead into a small pen during feeding time.