The Main Question
when a court case is decided in Louisiana, can it establish precedent
in other states that follow common law?
Yes.
The court decisions of a sister state are always persuasive authority. This applies even to trial court rulings and rulings from other countries that are not precedents in any U.S. state. Similarly, courts can look to legal treatises and sources like the Restatements of Law that have not been adopted or approved by any public official as persuasive authority. In theory, it would not even be improper for a state court judge in say, Texas, the quote from a Mock Court Brief of a law student as persuasive authority.
This is because the value of a persuasive authority (as opposed to in state binding authority of an appellate court) in states that follow common law, is that the reasoning of the ruling is intrinsically informative and is reliable because it comes from someone learned in the relevant law and familiar with the legal issues in question.
Someone could reasonable dispute persuasive authority from Louisiana on the ground that the substantive law rule in Louisiana expressed in its statutes and prior case law, which a Louisiana court is interpreting, is different from the law in the state where the Louisiana court decision is utilized.
For example, suppose that Louisiana has not statutorily adopted the equitable doctrine of laches which is a case law doctrine derived from English courts of equity which denies relief to people who make claims who have slept on their rights without taking legal action in a manner prejudicial to the defendant, even if no statutory statute of limitations applies. If a case allowing relief within the statute of limitations in Louisiana where facts justifying the application of the doctrine of laches were present in an Ohio case, it would be fair to argue that the Louisiana precedent should not be followed as persuasive authority, because Louisiana is a state that has not adopted the doctrine of laches, while Ohio is a state that has adopted the doctrine of laches.
But really, this means of distinguishing a Louisiana precedent is no different from the way that a precedent from any other state would be distinguished. Louisiana court precedents are not less persuasive on the theory that a court precedent in Louisiana's court system doesn't have the same effect as a court precedent in states with purely common law legal systems.
Furthermore, as explained below, while civil law systems in other countries do not afford the same status to appellate court decisions that common law jurisdictions do, Louisiana, in this regard, is closer to the common law system than it is to the civil law system, in any case.
Louisiana Law Is A Complex Civil Law And Common Law Hybrid