The Lunar Empire doesn't have a Navy as an independent service branch. The situation resembles the later Roman Army. The naval troops that invaded Karse from Corlfu were part of the Provincial Army, but they could have been originally from the Heartlands Corps like the troops serving in Pavis. The penteconters that patrol Oslir have soldier-rowers as crew, and are part of the Provincial Army or the Heartlands Corps. Some nobles could have their own war ships too. And if you want you can use smaller ships than penteconters. A marine is just someone who serves as a soldier on a ship, eg. the Greek hoplites that served on triremes weren't specially trained for it, they were just normal militiamen assigned for duty on ships. YGMV and you can make a small, less known cult, some hero cult perhaps, that specializes on naval warfare and boarding actions. Maybe the cult could have a spell that helps with jumping or climbing in heavy armour.
All officers in the Lunar Army must be members of the cult of Yanafal Tarnils, but all members of the cult of Yanafal Tarnils aren't officers. Every Lunar soldier must be at least a lay member of the cult in fact. And in the traditional Yelmic Regiments the rank and file soldiers are also worshippers of Yelm.