A person sentenced to life without parole gets the same number of appeals as any other person convicted of a felony.
They are entitled to one appeal before the California Court of Appeals. If that appeal is denied, they can ask the California Supreme Court to hear it. The state Supreme Court can decide not to hear an LWOP appeal, but they must hear a death penalty appeal.
If the defendant exhausts the state appeals, he or she may then appeal to the Federal courts.
Please understand that this is a general discussion of legal principles by a California lawyer and does not create an attorney/client relationship. It's impossible to give detailed, accurate advice based on a few sentences on a website (and you shouldn't provide too much specific information about your legal matter on a public forum like this site, anyway). You should always seek advice from an attorney licensed in your jurisdiction who can give you an informed opinion after reviewing all of the relevant information.
Any person convicted of a felony in California is entitled to one direct appeal. This is true regardless whether the person is convicted of a simple drug offense or a homicide with a sentence of LWOP.
After the Court of Appeal rules on a direct appeal, the defendant has the right to ask the California Supreme Court to review the Court of Appeal's decision. If the California Supreme Court denies review, or grants review but affirms the conviction, the defendant then may file a petition for writ of habeas corpus in the Federal Court asserting any federal or constitutional issues raised in the state appeal. The defendant also may file a petition in the United States Supreme Court to review the California Court's rulings.