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In the novel, he reads Cathy's diary just before falling to sleep.

I haven't read the book, but how would he know Cathy's name if it were a dream?

There are several things that Emily Bronte leaves ambiguous in the novel and this is one of them. It's never made clear if we're supposed to believe that it was Cathy at the window or juts Lockwood's dream. It's up to you, really. If I remember correctly Heathcliff never says directly that he's seen Cathy in the book, but, Nelly hears him talking to her and it seems that he's in conversation rather than a monlouge and at the end of the novel a shepard boy tells Nelly that he's seen Heathcliff with a woman on the moors, which shakes Nelly up. Although, at the very end of the novel she says she thinks the dead are at peace. So, take what you want from that.