We don't know for certain that Liesel and Max get married, but the strong assumption is that they do. We find out that Liesel marries, moves to Sydney, Australia, far away from all she has been through, and has a long life that includes children and grandchildren.
What we do discover in the book's epilogue is that Max and Liesel reunite after the war is over, in October of 1945. The scene unfolds as follows:
A man with swampy eyes, feathers of hair, and a clean-shaven face walked into the shop. He approached the counter. “Is there someone here by the name of Liesel Meminger?”
“Yes, she’s in the back,” said Alex. He was hopeful, but he wanted to be sure. “May I ask who is calling on her?”
Liesel came out.
They hugged and cried and fell to the floor.
We know this must be Max, even though he is unnamed, because Max is described throughout the novel as having “swampy” brown eyes and “feathery” hair. We also might think this because Alex is “hopeful” when he sees the young man who enters the store.
Max and Liesel had bonded during the several years he hid from the Nazis with her foster family. As the son of the best friend of Liesel's foster father, Hans, Max comes to Hans when he jumps off the train and escapes deportation. As Liesel is the one who has to take food to him in the basement, they grow close. They share a love of words and books and share their nightmares, which they both suffer from. As Max comes upstairs to escape the cold basement, it becomes clear he is a gifted storyteller. Liesel gives him snow as a Christmas gift and nurses him while he is very sick. They develop a very strong bond based on shared adversity.