An attorney, other than a public defender, who is selected pursuant to NRS 7.115 to represent or defend a defendant at any stage of the criminal proceedings from the defendant’s initial appearance before the magistrate or the district court through the appeal, if any, is entitled to receive a fee for court appearances and other time reasonably spent on the matter to which the appointment is made of $125 per hour in cases in which the death penalty is sought and $100 per hour in all other cases. Except for cases in which the most serious crime is a felony punishable by death or by imprisonment for life with or without possibility of parole, this section does not preclude a governmental entity from contracting with a private attorney who agrees to provide such services for a lesser rate of compensation.