'Lay' and 'lie' often get confused, especially in the past tense. So here is how to use them correctly:
1. 'Lay' always needs an object that is being laid somewhere. For example, 'I lay the book on the table.' The book is the object because this is what is being laid on the table.
In the past tense, 'lay' changes to 'laid'. For example, 'When John came home, I laid the book on the table and went to greet him.'
2. 'Lie' never has an object, because the subject itself lies somewhere. For example, 'The book lies on the table.'
In the past tense, 'lie' changes to 'lay'. For example, 'When John came home, Mary lay on the sofa.'