The Louisiana Rules do not require that all lawyer-client agreements be reduced to writing. Rather, the Rules require signed writings only for continent fee arrangements. See Louisiana Rule 1.5. However, a lawyer should require the client to sign an engagement agreement prior to commencing work.
For model lawyer-client agreements in contingent-fee and hourly-fee cases, click here: Model Lawyer-Client Agreements. The page also contains a form for an agreement to share fees among lawyers in different firms (in compliance with Louisiana Rule 1.5(e)).