Aha, you are right. I tried it on my LCD (16x2). I do get the double-quote but the backslash prints a different character. You will have to check the datasheet for your LCD and check its character map to see if it even has backslash and double-quote.
If it doesn't, most LCDs allow you to make your own special characters (usually 8 of them). You could make up your own backslash and double-quote and use those.
Pete