The Vegetarian Society has a list of E numbers and what they are. It says that L-Cysteine is an
Essential amino acid derived from proteins, synthetically produced, through natural fermentation, or enzymic processes, using raw materials of vegetable origin or pure organic, non-animal, compounds. May also be derived from animal hair and feathers. Used in baking to create stretchier doughs, especially for burger buns and pizza bases.
So sometimes it's vegan and sometimes it isn't.
This blog post is over 10 years old now but it did confirm that
In September 2010 the major animal source of L-cysteine was "human hair mostly" followed by "duck feathers or hog hair when the human hair supply was low."
If you like pizza, there is at least one company that says its use of L-Cysteine is vegetable sourced. So in general you'll have to ask.