Looks pretty cut and dried to me. Show SSR's maybe, so we can see what you're seeing? I'd expect the SSR's to have their own schematic so you'd know what to wire up.
From the drawing shown, Yes, an L1 is important.
nIf you trace the flow from L1 you'll see how there has to be one to form the circuit....
Welcome to basic electricity, please have a seat in a chair close to the front of the class...... (Just funnin' a little....)
I'm sure the teacher/s will be along shortly.