Livia has been accompanying Dan throughout his Journeys. Although they do travel together it is still unsure as to why they're time travelers and it is unclear as to whether or not we will ever find out.
Although it was identified that Livia died on a plane and no body was ever found, in actuality she disappeared. Nobody knew where she went and when Dan met up with her on his first journey he wanted answers. Later it was identified that Livia is from the 1940s and met Dan on accident. For some strange reason time wasn't letting her go back to her era so she adjusted.
It has been mentioned that Dan can go back in time and Livia goes to the future. There are conditions though, as they can only go backward or forward to times where they are alive. Livia has mentioned that the journeys will get longer.