What are the benefits in understanding the client's culture?

In answering your question, I assume by "clients" you mean Nao Kao and Foua, and the doctors in charge of Lia's care are the ones who would benefit from understanding Hmong culture, the ethnic group Nao Kao and Foua originate from. The central problem that leads to their daughter Lia becoming paralyzed is the lack of communication between her doctors and her parents due to differences in culture and English-speaking ability. The main benefit, therefore, of the doctors understanding Nao Kao's and Foua's culture would be better treatment for Lia and, as a result, the possibility of her managing her epilepsy well enough to avoid becoming paralyzed.
Nao Kao and Foua are not from California and speak very little English. They are from an ethnic group called the Hmong, who were vetted from China due to their refusal to conform to Chinese culture. The couple thus come from a very different world from America with unique customs and very little knowledge of the English language. In health care, communication is very important, as a patient needs to adequately communicate her symptoms to her doctors in order for them to determine the best treatment for her. If the patient and doctors don't speak the same language, this communication is all but impossible, and the patient is unlikely to get the care she needs, which is what happens to Lia. In fact, Dr. Ernst becomes so frustrated with his inability to understand what her parents are saying that he sends her away to a foster care center, a place where she then receives inadequate care, her epilepsy worsens, and she quickly becomes paralyzed as a result.
What The Spirit Catches You And You Fall Down ultimately demonstrates is the importance of understanding someone's culture in order to care for that person and have a meaningful relationship. This is true of not just in healthcare but in any relationship between two people with very different cultures. Lacking understanding of someone's culture can lead to miscommunication, which can then lead to anger, hurt, or in the worse case, as we see with Lia, grave injury. Even learning a simple list of Chinese vocabulary words would possibly be enough for the doctors to save Lia. Unfortunately, they are unwilling to invest in such a simple act of empathy.