Everyone knows that a writer should read, but the question is what?
The question I would like to ask here is: what books should a literary writer have read? What are the critical reference points that anyone in the game needs to have exposure to? What are perhaps lesser known works that are nevertheless important?
This is an open-ended question and clearly will entail a great deal of subjectivity, but writing is like that anyway.
So I don't actually think anyone could provide you with a useful list of books here, because individuality, different approaches, style, subjectivity, blah blah all that.
But an approach that works is this: read what you like, be it sci fi, fantasy, whatever. Harry Potter. Then sift through interviews and wikis of the authors you admire, and find their influences and teachers. Then read the stuff written by those. And enjoy it, but also, once you're done, ruminate on how they connect to the writing that brought you to them in the first place. Read them more than once if you have to. Good books generally need to be read more than once anyway.
This approach lets you get more directly at what you want to do, and leave out all the classic junk you don't really need.
Yes, it does take a little bit of effort - but hopefully you read enough for fun to have a list of authors you can siphon information from, even if one of them doesn't have a lot available. I mean reading a lot for fun is how you get to be a good writer. The best writers tend to read a lot.
It feels like you're asking for a literary canon, but really, I don't think there is one any more. Things are a lot more wide-open, with a lot less dead-white-male worship.
In terms of books that were really important to me (not that I'm a literary writer, but I tend to be a literary reader)... they've changed as time goes on. When I first read The Color Purple I was blown away by the dialect and the honesty, but it's not a book I've gone back to very often. I love re-reading Austen (Persuasion is my favourite) but I'm reading for the characters, not for the writing style, so I'm really not sure they'd help someone trying to read as a writer, rather than as a reader.
I agree with the other poster who suggested you try to narrow things down a little. Literary Fiction is a really broad category, but it can be broken down into sub-categories that might make more sense for you. Different cultural groups have different prominent writers - if you're African American, you should probably read Walker, Angelou, Morrison, Hughes, Wright, Du Bois, etc.. And it certainly wouldn't hurt for anyone else to read them, but if you're writing magical realism you might focus on just Morrison from that list and come to the others later, after you've read Gabriel Garcia Marquez and Haruki Murakami.
If you're writing some other sub-genre, I'd say you want to focus on other authors. So, really, it's pretty hard to pick one list that's going to be useful to everyone. Never hurts to read some Shakespeare, though!
Inferring that reading the right books can save someone from being a bad writer is ludicrous. Only repeatedly writing, and finishing, story after story can save someone from being a bad writer.
That said, all writers (all humans, really) should read equal parts fiction and non-fiction.
Fiction shows you how to write. As for specific titles, read whatever piques your interest, or is recommended based on your favorites. Setup a Goodreads account, add and rate the books you've read, and check out the recommendations.
Non-fiction shows you what to write. Read philosophies, histories, biographies, essays, and anything else of interest that exposes you to what individuals and communities think about their setting. This is food for original story ideas.
Which novels/stories you read is arguably less important than how you read. That's a topic for another thread.
It isn't what you read, but what you write that makes you great.
What do you mean by 'literary writer'? Do you mean James Joyce? Also, although we can identify loads of popular fiction that is bad writing, surely agreeing what is good writing and therefore choosing a list of novels is extremely subjective.
