Why does your leopard gecko try to escape her cage?

Yes. It can be handled. Put one hand in front of the gecko. Then, with the other hand, nudge it so that it goes onto your hand. Keep ypur hands still, and if it looks scared, cup one hand over it so it feels more secure. Never grab by its tail, as it will drop off. I would advise holding it with your hands inside its tank/cage, so if it tries to jump off your hands it will land in its cage and can't run away. At first the gecko will not like being held. Keep handling it and eventually it will get used to it and not jump down all the time.