|The idea of your poem is strong, but I think you need to build up more hope before that final, ringing truth: you're your own hero.
I'd say add more to the very beginning. Like, after "Rub the genie's lamp and all your dreams come true," go on to explain that wealth, those riches, that wonder! Talk about everything you can have, and the stability of being given what you need and want. Build up that desire, because that desire for the simple fix of the genie's lamp is what's going to make the end of your poem hit home.
I'd also say put 'there is no lamp' on its own. Putting it on the next line will make the audience pause, and again, sort of build up the loss. You could also add more about what it's like, not having that quick fix, that stability of a 'magic lamp.'
"When you don't have a genie,
you have to become your own hero (remove period)
Because not everyone can find a magic lamp.
this should stay the same. It's final, simple, lovely in its little tragedy. Such a good end deserves more to build it up, though, and I get the feeling when I'm reading this that a lot wasn't written down. There's more to this lovely little poem! I hope you work more on it.