if I build a Trident in full game mood > then I only pay lite game mood next > then can I keep and use my Trident in lite mood?

Yes and no.

Under current mechanics you will not lose your trident if you downgrade to a lite-subscription, however, you will not be able to fly it.

There is always the potential that this could change in the future, possibly via spending Crystal, but that is not the current state of things.

Easy fix: Just pay up. This game deserves the payment, so if you are going to play long enough to build a Trident, then pay the full price to fly it.

I would suggest answering the question yourself after the 4-6 months of hard work and full subscription that it takes to build a trident.

If you are serious about investing that much of your life into a game, doesn't it make sense to support that game?

I do wonder what happens if you're already out in your trident when your sub downgrades. My expectation would be that you can continue flying it around until it either dies or is docked, at which point you'd find yourself unable to launch it again.