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Draw the enclosure in its most closed position
On a simple plan, mark the roof, fixed walls, openings, screen type and positions of any movable glass or panels. Take a photo from the open yard and another from inside the patio. A set of sliders that can be opened when convenient is a different proposal from an opening that will remain permanently clear.
Use the appliance’s definition of outdoors
The Outdoor Lifestyles Lanai manual provides specific examples of permitted outdoor configurations. For a covered space with three sidewalls it specifies a minimum permanently open portion of the perimeter. It also identifies two mesh sizes it accepts and excludes solar and no-see-um screens. Those conditions belong to that model family. Other outdoor fireplaces can have different limits.
Resolve the fireplace and enclosure together
Give the exact manual and the drawing to the fireplace professional and enclosure designer. Ask how the planned work affects ventilation and clearances and who will confirm suitability before use. If the space has already been enclosed and compliance is uncertain, leave the appliance off until the enclosure and model are assessed together.