Hard to say. Would depend on how bad the depression was. As a few people have said, whilst money doesn't necessarily buy happiness, the lack of it brings misery. Money issues/financial problems are the reason for a LOT of stress in peoples lives. And stress leads to depression.
Whilst there is no guarantee a big lottery win will lift someone out of their depression, it would certainly be a massive positive in the lives of most people, as it would bring financial security and freedom, and mean they could leave their job and never have to work again.
Never having to work again would make a LOT of people happy, as many people hate their job, (or just tolerate it even if they don't hate it!) Doesn't mean you will sit on your arse all day watching TV, many people would be able to do something they enjoy/want to do, like writing, art, pottery, woodwork, making clothes etc, or they could start a little club that people can join to do any given hobby.
Or maybe start a dance class or aerobics class, karate, judo, boxing etc etc... Or a little gardening business, or whatever they want to do. Instead of working for someone else in a job you don't like much, lining someone else's pockets, often getting minimum pay, (and very few holidays,) always having to meet targets and goals, and never getting any thanks or reward. (Or rarely anyway!) And all this, just so you can pay your bills!
If I had millions, I would love to start a little book publishing company, and sign up unknown writers who can't even get an agent, let alone a book deal. DH would open his own comic, sci fi, and model shop (like Forbidden Planet,) and I would help him. We don't have anything like this for 30 miles, so it would be great! If money wasn't an option that is. As I say, we'd give up our jobs but would still 'work...'