Laura meets with a therapist because she wants to do something about the path her life is taking. The doctor tells her to lie down on the couch, relax, and say whatever comes to mind. This psychoanalytic method is known as:

psychoanalysis method (therapy)

Explanation:

The psychoanalysis method was proposed by Sigmund Freud. This method work on the unconscious mind. In this method, Freud lay down the patient on the couch and told them to get relax and close their eye, s and say whatever comes in his mind. This is the method through that patient reveals their experience related to their childhood. In psychoanalysis, the therapist took 2 to 5 sessions per week.

Thus here Laura meets the therapist called psychoanalyst who conducts therapy called psychoanalysis.