Who did Lockwood think Cathy to be? How did Heathcliff correct him?

Trying to make conversation again, Lockwood gets into trouble first assuming that the Cathy is Heathcliff's wife, and then that she is married to the young man, who he supposes to be Heathcliff's son. He is rudely corrected, and it transpires that the girl is Heathcliff's daughter-in-law but her husband is dead, as is Heathcliff's wife.