One last one...

Larry fell asleep two minutes after he had (laid) down.

Should it say lain down due to no object?

Right! It should be had lain down.

You've mastered some difficult concepts in these sentences. :-)

To determine whether "laid" or "lain" is correct in the context of the sentence, let's first clarify the difference between the two words:

- The word "laid" is the past tense of the verb "lay," which means to put or place something down. It requires an object, so you could say, "I laid the book on the table."
- The word "lain" is the past participle of the verb "lie," which means to recline or rest in a horizontal position without an object. For example, "I have lain down for a nap."

In the sentence you provided, "Larry fell asleep two minutes after he had (laid) down," we need to use the past participle form of the verb since "down" does not indicate an object. Therefore, the correct word to use is "lain." The corrected sentence would be: "Larry fell asleep two minutes after he had lain down."