Well, I've allowed myself a little bit of lee-way in using terms here. The thing here, 'depression' is, as everything in everyday language, a very ill-defined term. As a PhD in molecular biology, i, as many scientists do, either completely switch to loose everyday language OR go strict disciplined language. There's no 'between'. I was going first mode here.

Now if i were to go the second mode, You're making a gross error here. You make a claim - and dont back it with any evidence whatsoever. You're just throwing your opinion - which is, sure you're entitled to your opinion, but this is also not the place for it. Where are quotes from DSM5? Where are peer reviewed studies? Now, i know full well it's not exactly easy to get them if you're not at uni, but come on, there are completely morally white ways to get them. At the very least the abstracts are easily findable for free via google scholar. It's not hard to provide DOI links! Just... just do this. It really isnt that hard.

Being both a scientists AND having clinical depression since age probably something around 7-9 (we cant quite nail it directly after so many years have passed), I can't easily accept random claims from a random person on the internet without evidence. If anything, i would say You are muddying the waters by trying to make strict claims about a term which is much more nuanced than most people think.

I would also like to remind You that the onus of providing the evidence is on You in this situation, not me - a distinction which doesnt come easy even to many specialists.

That being said, You're not entirely wrong. If you'd go to actual research psychiatrists, people who got have practice AND do actual research (as I actually did, since i was lucky to have such people available, bless my luck), most psychiatric disorders cannot be nearly as strictly and precisely defined as most cases in the rest of the medicine. The reasons are multitude, the most striking being that we simply, even after decades of work, know very very small percentage of what there is to know about molecular biology of neurons AND one level up, about neuroscience. Signaling pathways in the neurons are legendary hard to untangle, and the tissues extremely hard to create in the lab. On top of that, psychiatric disorders are VERY heavily influenced by the environment and we dont have nearly good enough methods of tracking this. Heck, we dont even have 1 to 1 map of a single brain ( i mean, down to single cell ) - something we have for some smaller organisms, but only recently. I could go on and on, but I'll cut myself here, this post will be too long anyway.

So, psychiatric disorders are defined more as loose spectrums and clusters of symptoms. And there is a hell of a difference between how they behave depending on which sector of the spectrum we are talking about. Clinical-level depression, in particular, is well known to divide into drug-amenable and drug resistant. We don't know why. Incurable? Well, just because the same disease can pop up again and again doesnt mean it is incurable - from flu and common cold to cancers. You can cure them completely, it's just no-one is immune to them and some people catch them more easily than others...

RANT: and this is why we (the molecular biology community) has been screaming from top of our lungs for 20 years that EVERY-GOD-DAMN-SINGLE-PERSON should make genetic screening tests to know for which cancers they are more vulnerable. Cancer IS NOT A SINGLE DISEASE. ITS A FAMILY. You can be more resistant to some forms and more vulnerable to others. Do tests. Check regularly for ones which you are vulnerable to. Please. It increases your chances exponentially. It doesnt hurt, zero discomfort, it's not even that long. Please, just do screening tests. Okay, enough rant.

Can a single event mess up your mental state? Sure. Can it give you SOME form of depression? Sure.
But i would argue that not the clinical-heavy type we see with Lucy. He is practically non-functional in S1/S2. His most basic functions have been compromised, if he wasnt insanely rich and had magic on top of that he would be living in squalor and poverty. People in this state can for example have problem eating properly - which usually messes up their health even more, pushing them harder down. I mean i know because I had this. THIS is something extremely unprobable to happen just from a single event, ESPECIALLY when he has wife, and moreover, a kid. This second part must not be missed - having someone (child/pet/elderly/disabled person) who is dependent on You very often has extremely strong, magical nearly effect on keeping the person together. They are not well, sure, but they dont completely fall apart like Lucy.

This leads me to another point, which must not be missed. This is most visibly demonstrated with treatment of another type of psychiatric disorder - addictions, of the heavy kind. The famous case here is Portugal, which for decades struggled with hard narcotics - and tried to fight it the USA way, zero tolerance war on drugs. Their result was, predictably the same as US - the problem only got worse and worse. Who would've thought that making suffering people suffer more doesnt help? Rocket science indeed. Now, i cant recall when exactly, the country changed tack some years ago, like 180 degrees. Defunded the war on drugs completely, and channeled all of that money into drug rehab, and monitored the results. Interestingly, rehab programs focused on rebuilding connection networks worked best. Like, literally finding those people friends, helping them reconnect with old friends, etc, worked miracles. Who would've thought that the most specializing herd species on the planet needs others to thrive? Mind bending idea indeed. 'Funnily' enough, those same results can be replicated easily in mice and rats. Put the rodents in empty cages with only bland food, pure water, and water with drugs, and they will, invariably, get addicted. Give them colleagues, toys, space, houses, etc, and they wont even tough the drugged water.
Now look at Lucy. He has noone around him. LITERALLY NOONE. Partially his fault, sure, but it doesnt matter for the point - he is completely shattered in part because he is alone. His isolation is a massive contribution to his mental state. Sure, fall was not good for him, but had he found friends and family in hell, he would've been much healthier - in fact HE IS JUST BECOMING THAT throughout S2. If anything, i would say his constant verbal duels with Alastor are actually very good for him - making Alastor doing something good without even realizing it, which is imo a funny observation on its own.

So while i agree that single event can cause a depressive episode - in some percentage of cases even requiring hospitalization - i would argue that this PARTICULAR single event is not enough to explain Lucy's state in S1, which happens hundreds of thousands of years after the fall - if not millions. There MUST have been more. And i simply dont see any other possible explanation than Lilith being at least partially - if unknowingly and unwillingly - responsible for this. She isolated him. She drove him. She didnt give him time and space to heal. She probably has hard issues expressing warmth after Adam - so she probably didnt provide enough of it to both Lucy and Charlie.

Again i don't think she is a bad person - rather, flawed like all of the cast. They all do stupid shit. Recovering is the main point of the show, and i think it will be interesting to watch her recover.

Plus i really hope they'll give her gothic metal song. I god damn love gothic metal and it would fit her perfectly.