The nightmares the old doctor created were not (at least not openly, although there might have been undertones) of a sexual nature. What exactly they contained is open to ideas and suggestions, but it is likely they were influenced by books, plays and themes popular among Victorians. There was a much interest in fairy tales and folk legends, for example, which could be twisted into nightmares, crimes (the Ripper murders, to name the most famous example) impressed people's imagination, there are fears common in most people's recurring nightmares we could use. Whatever contains an element of horror might be a source of inspiration.
The dreams created by your character would initially (while he is still learning the technique) be closely linked to those dreams the old doctor frequently used and thus firmly established, but we could change them early on and create new and very different ones. These, too, need not be of a sexual nature, but the erotic aspect of the dreams attracts me as it would create a 'world' in which, without inhibition or consequences, the wildest, strangest fantasies could spring to life. It might even be an interesting possibility to later have their dream experience and reality overlap, I find it strangely intriguing to imagine them having rather vanilla sex in their physical reality while at the same time, in her mind, she is ravished by a dream creature which in his mind is him...
Also, it might be noteworthy that I by no means intend to make Elizabeth a tragic, melancholic sufferer. She is a healthy, normal young woman in her early twenties, the melancholia the old doctor claimed to have diagnosed and treated was nothing but the pretext for and consequence of his experiments which resulted in her spending not a single night without being haunted by nightmares, thus sleeping badly - and finding hours of her days dedicated to reliving and describing some of the nightmares and hear him analyse and interpret them - and her. With the old man's morbid influence and habits removed, there will have been an instant improvement. Elizabeth might well be a lively, strong minded, witty young woman with many interest and every intention to fully enjoy her life.
Her role in her dreams will be by no means a passive one, either, she will experience them and act in them as if thrown into a different reality, as such is the nature of these dreams. It also is how your character will experience a dream once it is begun and he has ventured into it, the dreams will be vivid and seem completely real to all senses, no matter how surreal the setting and events. Only he, as the creator of the dream, can influence and end these dreams at will.