My [28F] roommate [30F] eats all my food. Even the food I've hidden in my room.

I signed a year lease when I moved in with her so there's no way I can get out of this until months from now. It's only been less than 4 months and I cannot deal with this woman anymore. I think she has some kind of eating disorder. We're not especially close and I haven't known her for long, so I'm hoping for some advice about what to do that won't cause drama.
She goes on binges where she eats everything in the apartment. It doesn't matter what or where it is. She can clean out the fridge and cabinets (week or so worth of food total) in a single day. This happens at least a couple times a week. She spends all her money on takeout, fast food and cornerstore junk, then complains about how she never has any money. If she didn't have automatic payments set up she would probably not make her share of the rent each month. She's had to ask me for cash for things like gas, which after never paying back a couple times, I've stopped lending.
I've never seen anyone spend so much on food for one person, she buys like she's stocking a bunker or trying to feed a family reunion. She started taking my food shortly after I moved in, this was in September. First it was just one item going missing here or there. I thought I misplaced them or didn't remember finishing them. Then she got more brazen and would pass it off as not realizing things were mine, claiming it was on "her side" of the fridge. Things like that. I said if she wasn't sure then please ask me. I don't have a lot of money. She said she would. Never has. After that she more or less stopped trying to hide what she was doing at all. She's been eating everything I get for myself, on top of a half-dozen+ food trips per week for her own stuff.
Like I said it's all junkfood and I don't get much of that for myself, but that doesn't stop her. She'll eat whatever I buy. One shopping trip I deliberately bought nothing but lots of veggies and other ingredients for healthy meals like salads, omelettes and stir frys. I thought she'd leave at least some of it alone given her preference for sugars and fried food. She still ate all of it during that night. Most of her eating happens at night when I'm asleep, or in the morning when I'm in class or work. If I want to eat (like cook an actual meal, not grabbing something on the go), I basically have to buy my food and make it during a window of time in the afternoon when I'm at home while she's at her part time job. Otherwise any items I bring into the house will be eaten as soon as I'm away or asleep.
The last straw has been this week. I started just storing non-perishables and non-fridge items in my room. (Yes I did keep talking to her a few other times about taking my food when she kept doing it, but nothing ever changed so I gave up. I honestly think she can't control whatever problem she has.) Now I found she figured it out and has been raiding my room for food when I'm out of the house.
I may put a lock on my door (have to ask landlord first) but am I wrong for thinking it shouldn't be at this point? It's extreme and not sustainable for my budget. I was considering sitting down with her and telling her that I think she should talk to a doctor about her eating behavior. I'd of course do this calmly without anger. I think she's ill in some way and the compulsive eating is a part of it. I can't know if she's depressed, but physically she's well on her way to morbid obesity if not there already.
If she isn't willing to talk to a professional then I'd try to get a lock for my door, but I figure I should first try encouraging her to get help.
Does this seem like a good approach? Anything else I could try? Thanks for reading if you made it this far.
TL;DR I live with a roommate who binge eats all my food whenever I'm asleep or not home. My past attempts at telling her to stop haven't worked, and I think she's suffering from an eating disorder or other illness.


Source.

Sounds like you need to give her a sammich....a knuckle sammich

Footlocker and mini fridge...both with a lock.