"Don't lean close to me!"
Can someone please come up with a situation where I can use this phrase?
No, that sentence (in English) doesn't make sense. According to another discussion what the Chinese sentence means is 'don't come close to me'.
The English translation is odd. It should be more like "don't come near me".
I think the lean in thing was done as to not confuse learners to think 靠 means come. Because it doesn't. But it leaves us with a weird English sentence.
You may be right, and the Chinese means something more like "Don't get so close to me" or even "Back off!" But we do say "Don't lean on me" or (for the opposite) "lean in, I want to tell you a secret". Could 靠近 be used for those meanings?