Jasper is a dream walker, As a dream walker he can enter anyones dreams as long as he has a strong bond with the person. In the world of this story everyone can dreamwalk so it isn't an amazing or rare skill. Jasper enters Lili's dream and is surprised he is able to do since the last time they met their entire relationship ended terribly. Jasper and Lili weren't lovers but friends, a friendship that meant more to Lili than it it did to Jasper. Not to say he didn't care about her or didn't have the same feelings but Jasper refuses to get close to anyone and felt he needed to distance himself from her something Lili feared. At this point of the story both character are battling with their own issues and neither are open to one another until it was to late. They used one another as an emotional crutch.
In dreams we feel sensations and emotions, For the dream to feel real to Lili her subconscious created a world in which these sensations are felt such as pain. For Jasper to leave the dream he must be removed by force. No one was able to get as far as Jasper has meaning he is a large threat. Jasper isn't afraid to fight back but is aware that the idea of dying and the feeling of pain feels real even if he isn't in any danger. Jasper knows he only has one chance and refuses to back down or die no matter how painful the actions are.
There limits to what Jasper can do in Lili's dream. He can alter somethings here and there but nothing drastic enough to be consider important. Jasper can't read or tell time because it doesn't reflect reality. Lili believing she is not dreaming doesn't have these limits and she is able to help Jasper in many ways including understanding the world. The subconscious has a strong grip to the dream, it controls everything and everyone the only disadvantage is it gave these figment of imagination a will and choice believing it would help Lili to keep believing everything and everyone around her instead of it being lifeless souls wondering about. This pushes many characters within the dream to make good or bad decisions especially those who hold her memories. Once Lili gains her memories she slowly can alter those around her. So Jasper and Lili must keep moving further and further away while collecting her core memories so she can have enough strength to awaken before its to late.