Place the lamb in 6 cups of water and bring to a boil. Lower heat and simmer 1 hour, skimming off any fat/foam that may develop.
Add the barley and cook 15 -20 minutes. Add more water any time the level drops below the level of the lamb.
Add the split peas and cook another 20 -25 minutes. The barley and peas should be nearly soft enough to eat.
Remove the lamb and bones and set aside.
Add the vegetables and cook another 20 minutes.
While the soup continues to cook, allow the lamb to cool, then remove the meat from the bones.
When vegetables are tender to your liking, add back the lamb meat and the spinach if you are adding that. Heat long enough for meat to warm. Serve with good warm bread and butter or cheese. Even try Manchego, a hard, flavorful sheep's milk cheese! Note: if you use beef or even chicken broth, the soup will taste less like lamb and more like beef or chicken than I think it should. If you have to add broth/bullion, try vegetable. The lamb bone is important for flavor and the peas will cook down and help flavor the broth. The peas and the carrots add color to the broth, too, so don't despair if the broth looks a little "empty" at first.
This recipe came to me from my Irish mother-in-law, who passed away on January 20th at age 96. Her first husband was Scots-Irish, and the couple lived for a time at her mother-in-law's boarding house in Rockaway, NY. I don't know for sure, but I imagine this is "Mother Reilly's" recipe, served to her lodgers to warm them on cold winter nights. I hope it warms you, too.