I get where you're coming from, Kho. Lay (and fell) are probably better words to use in the examples I gave.

Wiktionary is at least telling me that [url=https://en.wiktionary.org/wiki/lay#Etymology_4]lay[/url] and [url=https://en.wiktionary.org/wiki/lied]lied[/url] can be interchangeable. The pages on lay and lie are fraught with all sorts of interesting stuff, including notes on formality, so I'm going to go looking some more. Watch this space!

Edit: By the way, 'lay' is still transitive only.

Edit2: LIED AND LAY ARE NOT INTERCHANGABLE unless you are speaking informally. Read on.