Your S.T. Dupont Minijet lighter does not need much maintenance. To restore its original shine, you can clean all types of coating using a soft cloth (never use solvent-based products).
For all silver-plated parts, use a special silversmith’s cloth, available commercially.
For all-natural lacquer parts, do as you would for glasses lenses, or jewelry. Mist up the surface and rub with a soft cloth. The lacquer is practically impregnable by acids. It is incredibly hard and resistant to impacts, scratches, friction, and water.