Is it ok to mix an oil additive to fully synthetic oil?

It's perfectly fine. If anything, it's gonna provide better wear protection if you use it.

The problem with synthetic is people have been told it is quite acceptable to run over 20,000 miles without an oil change (filters only). The filter system is set up on a bypass system. Not all the oil is ever filtered, thus the particles and acid are still allowed to build up causing wear. While the synthetic does a great job of masking the wear, there is significant wear, nonetheless. I have bought several used vehicles that should have had a lot of life left in them, but when I did an oil change back to regular motor oil, the wear on pistons, cam chain, etc was revealed and the engines needed rebuilt. I suggest that for the longest possible engine life, use regular motor oil and change oil and filter every 3,000 miles. I also add a small amount of oil to each tank of gas (1 to 2 oz. of any clean, new motor oil). Some prefer Marvel Mystery Oil, but I can't justify the added expense.

Lucas is a full synthetic additive. No problems there.

I don't recommend it. Synthetic oil is hard to improve - being synthetic they make it that way, you know.