Lay, lie.. Aren't they the same?

So when do you use lay and when do you use lie? The difference is the following:
The verb "lay": lay-present, laid-past, laid-past participle
It must come before an object since it is a transitive verb.
For example:
Future: I will lay the book on the table.
Past: I laid the book on the table.
Present Perfect: I have laid the book on the table.

The verb "lie": lie-present, lay-past, lain- past participle
Since it is an intransitive verb, it does not need to come before an object.
Future: I will lie on the grass.
Present: I lay on the grass to rest a little bit.
Past: I lain on the grass and felled asleep.