First of all, there's nothing wrong with the way you asked the question. The same confusion could easily arise among native speakers. "Let me know when you're leaving" can mean both "tell me what time you plan to leave" and "at the time when you leave, let me know." Because the message can be understood either way, your friend may have felt that it was safer to assume that you wanted to know right away. You could make your meaning more clear by saying "Let me know when you leave school." The phrase "when you are leaving" can be interpreted in two ways ("the time when you will leave" or "at the time when you actually leave"), but "when you leave" is less ambiguous, and would generally be understood to mean "do this at the actual time when you leave." You could also make it clear by reversing the sentence structure: "When you leave school, let me know." There's no chance of any confusion that way.

'Text me when you are leaving school' ! or 'Text me when you leave school' otherwise, 'Let me know when you leave school'

there is nothing wrong with the way your text was replied to. "I'll leave at 4" and "I will leave at 4" and "I am leaving at 4" are all the same for your context. (of communicating) You cannot send a text your friend to force them to reply in a certain manner that you expect or prefer. Most native speakers would respond with a similar text. Or the same text. For texting now we say "text me" instead of the traditional "let me know"

One way to be more precise with the timing of a request is to use the word "right." As in: "Let me know right when you leave." This signals a request for a response at a particular time, not just information about when they plan to leave.

well, 'let me know' means like 'give me the information' so it's more natural to say 'give me a shout/text me when you're leaving/when you finish school' However, if you want to know the leaving time now, you should say 'When do you finish school?' or something.. She's not a native speaker too, because she said 'I will leave at..' which we don't say, ha ha - so many chances for confusion. :)