Liselotte and Enrich's relationship began a lot of time before the main story starts. They get along very well even if they have different personalities, and the help each other when needed.
When they meet, he saves her from a witch, and when she sees him, she recognizes someone of her past, maybe a childhood friend, and calls him "En-" because she can't finish her phrase not being sure about it. Since he was starving, Liselotte takes him in her shoulders and get him in her home as a guest. Though he says that his name is Engetsu, she's sure that he is her old friend Enrich, but anyway, he tells her that she can call him just "En".
He will start to live in her home and he will help with any help they will need. With this, their relationship starts to become more and more romantic.