C. Client's is the correct choice.

Reasoning:

1. Client: This is a noun used to describe a person who engages the services of a professional, such as a lawyer. However, without the possessive form, it does not fit grammatically in the sentence.

2. Customer: This noun describes someone who purchases goods or services. In legal contexts, "customer" is not appropriate as the term usually used is "client."

3. Client's: The possessive form "client's" indicates that the prayer (a formal request to the court) is made on behalf of the client. In legal terminology, a "prayer" is a specific request or demand made by the lawyer for the court to grant some relief or judgment in favor of their client.

4. Customer's: This option is incorrect because "customer" does not fit the legal context. The term "customer" is not typically used in legal settings when referring to someone who seeks legal services.

Summary:

- The correct form is C. Client's because it correctly indicates possession and is appropriate for a legal context where the lawyer is making a request or prayer on behalf of their client.