OK, so, in the patient lounge, there's a sign that's a noose with a red "no" symbol over it. That clearly implies "no self harm or suicide allowed". However, they occasionally let their patients have objects that they can, and do, cause themselves significant harm with. Why aren't they being more careful with that stuff?
Example 1: Dolly with knitting needles, inflatable bats, and even paintbrush handles.
Example 2: Lilo. Choose play therapy at the wrong time, and you'll give him a wooden "ball-on-a-string" type toy. He will promptly proceed to hit himself in the head repeatedly with the ball, possibly on purpose, and will show up outside afterwards with bandages wrapped around his head and with his progress considerably hindered.
It's possible that these objects are only allowed under supervision (since the patients only gain them while in session with you), but in real life much safer alternatives would typically be used in such exercises. It can also vary depending on whether or not a patient has shown actual suicidal tendencies before.
The in-game analysis states that Lilo has been normally communicative for most of his time with his owner and has only recently started showing symptoms. Question: why is he assumed to be autistic? The diagnostic criteria for autism requires symptoms to become apparent when a patient is very young (or, I suppose, when a cuddly toy is very new.)
In my (non-professional) opinion, PTSD might be a better diagnosis for him; his symptoms started after an event that was traumatic to him, both because of the teacher's actions and because he believed that it was his fault that his owner failed her math test. Your mileage may vary, of course.
Or perhaps reactive mutism? Either way, there is no reason not to assume that Lilo has been autistic for all of his aware life - autism is not a disorder that can be cured, contrary to the game's portrayal.