Didja really think we'd just twiddle thumbs for months knowing this was coming? Discord questers have been discussing for months how to make this happen. Prom already confirmed we'd have, at the very least, enough for a naval battlegroup of battlecruisers, carriers and some lighter warships, plus a sizeable ground force.
Can we save Rasalhague? Not really, maybe if they were next door neighbors. At best we can slow the invasion, but ultimately, no matter how many fights we win, itll be a fighting retreat. We cant afford to be encircled, even with naval dominance on our side. We still need friendly neighboring worlds to maintain supply lines. But that's all assuming the rest of the IS just drops the ball and does nothing.
This was the whole point of contacting Rasalhague. We had a logical excuse (first try failed, second go bogaloo) even without in-universe knowledge of clans. It's also why plans to diplomacy lyrans are also considered. They can help us maintain a logistical corridor. Tikonov should be scared shitless after what happened to FS, and the capellans will support logistical stops in their territory. Caps alone should answer half or so of the journey for us. For logistics, we'd really only need the most sensitive (warship) or unique (petrusite) supplies from the republic itseld. Anything else like food, medical supplies, etc can be bought local.