There's a million and one ways to catch a fish, so you have to decide how you like to fish and what you want to fish for, and then zero in from there. Trolling in may successfully usually requires downriggers. Jig fishing requires an electric motor to hold your boat in one area.
Depths? Depends on weather and water temperatures. But generally, Lake trout will be from 40 to 120 feet. Daily. Kokanee from 20-50, daily. Bass along the banks. Rainbows along the shorelines, especially near creeks or boat ramps. (Sheep Creek) Bass, they're small smallmouths, in the rocks.
Rainbows, Kokanee, and very small lake trout (under 25 inches) are the eaters, bigger lake trout that are big enough to eat other fish and slowly grow into monsters are to be released. Be sure to have any boat you tow in inspected, and be sure its clean, drained, and dry to prevent any spread of mussels. Lucerne is in Utah. If you go north, you'll need a Wyo license too. You'll also need a Wyoming AIS sticker on your boat if you go north from Lucerne ($30).
Just some starter information. In May, bring your snow gear. Seriously. It can do that, and has every single May I've lived here (26 years). It can also be sunny and 80, so plan accordingly. Winds blow hard, commonly 15-25, and at times up to 50 or more. Always have an escape/shelter plan.
Should be a good time if the weather cooperates and you can avoid the big crowds. If you're here on the 19th-21st, get as far away from Lucerne Marina as you can, as fast as you can.
you may need to fish for rainbows and bass
I don't fish for rainbows alot but sheep Creek by the boat ramp is easy to fish for them
get a map Fish n Map co. of flaming gorge res.
we don't know how you fish are what you know. look at you tub on fishing at flaming Gorge.
If I'm around Flaming Gorge when you are there I will take you fishing for kokanee one of the days. you guys will need to buy a $10. WY. Stamp. I don't go there much on week ends
Just PM me