Your understanding does provide the basics but here are some examples.
"You said you liked pie but when I gave you some you didn't eat it. Did you lie (to me) about liking pie?"
The verb "lie" can be used with or without and object. When used with "about" it expresses the event that spoken falsely. When used with "to" it expresses who was told a lie.
"It looks like gold but you can't fool me. I know pyrite when I see it."
"Slight of hand are magic tricks that deceive viewers into believing something false."
"Fool and deceive" are synonyms that require a direct object. You have to say who was fooled or deceived.
The word "lie" does not require the same rules so the three words are not interchangeable. However, you can usually interchange "fool" and "deceive" though "deceive" is a little stronger than "fool". If you fool someone it is usually something funny or minor such as a prank. When you deceive someone the event is usually more serious but you can see in my example that it doesn't have to be something serious.