This is the dome light on my boat. If you have red/white dome and spreader light switches on yours it is probably the same. You may be able to find replacement LED bulbs. For me I left mine alone - they are working just fine.
This dome light gets a lot of discussion on GG site. The original fixture is no longer available. Switches available from DigiKey. Some have replaced the fixture with LED's but mounting will be different and they won't ship with spreader light switch. I prefer to keep mine original and not make a project out of it.
Try these threads.
www.greatgrady.com
Be careful with single LED replacement lamps. LED's tend to be very directional. The replacement fixtures have several LED's to scatter the light around.