I hate to put her in a position where she may lose a job she desperately needs but I don't see another option if she isn't willing to address the problems I am having with L.
This is a false dichotomy. You've stated that there are two choices, either you put up with L's antics or she loses her job. There are tons of other options. You may be the only full-time sitter that she knows of know
but you aren't the only full-time sitter in the world. If she has to find another one, she can. Honestly, I think that losing you as a sitter is one of the few things that will get her to pay attention.
Question: When you say that he's sneaking the bad food, is this coming in in a back pack or something, or is it in your home. If you want to continue taking care of L, I suggest that you: 1) Remove all of the bad stuff from your home or lock it up, and 2) Search his overnight bag and confiscate bad food. I realize that both of these are unpleasant for you, but if you're going to take responsibility for this kid, then you need to do the whole job. Saying "I can't do anything because he does this after I go to bed" is abdicating the full responsibility.
Do you have a medical POA for L? I'd refuse to have him unless I did. If you need to call an ambulance because he goes into shock, you won't be able to authorize treatment otherwise and you'll have to wait for her to give the authorization, which puts L very much at risk. I read in an earlier comment that you're unwilling to "discipline someone else's child." Are you willing to be sued for everything you have because something goes wrong and you were unwilling to take steps? Sorry to be a negative Nelly, but this could turn out very, very badly for you. You're accepting responsibility for someone in a fragile medical condition, but aren't willing to take action to prevent problems. If someone hands responsibility for a child over to me, then I am in loco parentis
and I will discipline as needed; if they don't want me disciplining their child then they need to keep the responsibility -- nobody gives me responsibility with the matching authority.