[PTTG]

The gate is 100km wide. Nukes (and other defenses) are not really adequate at those ranges in space.

Plus, the Lethrani are not naïve of diplomacy. They deal with the two smaller enclaves and a number of independent states, and realize that being too hasty would only ruin this chance and lead to destruction. So, they are trying to establish space control through diplomatic means.

Finally, when it comes to a shooting war, their TL advantage (they are a mature TL9 in fields the GM feels are relevant) comes into play. Taken together, we can assume they have significant defenses on the Earth side of the gate (said gate survived at least 10,000 years of disuse on the lunar surface, so it's probably pretty tough), when the war starts. The plucky heroes might need to cross the lunar terrain in buggies and on foot to disable these!

No doubt some factions would attempt to modify existing nuclear missiles to have the delta-v to reach the moon and back, but that would take a lot of time and work on its own.

It should be noted that their technology is a bit backwards in two fields: medicine and computing. Their medicine is actually early TL-8 at best, due to a general fatalism. The computing tech is incompatible with Earth tech, but not much more powerful, despite the generally higher tech of Lethra Koas. This is probably due to less focus on consumer electronics to drive costs down.