Occasionally they just need tubed until they eat enough solids to survive.
My understanding is that, although a hungry very young lamb will eat creep and hay in a desperate attempt to stay alive, their rumen isn't fully developed until 5-6 weeks old, or older, so that a lamb not getting milk until then won't be getting what it needs for health and growth.
I just wanted to clarify that in case people reading this thought it would be okay to leave a lamb that won't suck if it seems to be eating cake and hay.
I'm not sure I could bring myself to tube-feed a lamb for 5-6 weeks though...