The plot revolves around a wargames scenario. There is for some reason an alien race that is really good at war strategies. There is an advisor from that race on the enterprise.

Ah, that would be “Peak Performance”, in which Wesley has an experiment that has something to do with high-energy plasma reaction with antimatter, and nothing whatsoever to do with growing dilithium. Swing and a miss.

The Klingons use Trilithium.

Strike two - trilithium is an unstable explosive that is used in the engines of exactly no one. The Klingons do use tritium as an intermix, but as you are aware, that simply replaced the role that deuterium plays in Starfleet designs - it has nothing to do with dilithium.

The Romulans used a contained singularity.

This is the closest you’ve come to having something. Of course, there’s exactly zero information on how those drives operate or are manufactured, along with the pesky fact that the Romulans have enslaved an entire race to mine dilithium for them, which is…not something you typically do to obtain a substance that you don’t need. We’ll call it a foul ball.

In Voyager we saw a number of potential non-dilithium alternatives. One of them was a glorified slingshot.

What did we learn about how these alternatives are powered, particularly considering that several of them were plugged into Voyager’s warp core without too much trouble? You get bonus points if you can identify the one that was specifically described as “not antimatter,” which is most likely (but not guaranteed) to exclude dilithium.

So far we’ve got two strikes and two fouls. You’re still at bat.