I won't try to contradict the tactical analysis of my more aerospace savvy peers, but it's worth thinking strategically about the Leviathan as well. As noted, it's very short legged, and yet very hungry. The best strategy would simply be, as in baseball, him 'em where they ain't. If the Leviathan defends a world, attack another. If you're feeling cheeky, hit a nearby world, let the big monster scramble out to meet you, then run. If you're feeling really cheeky and have access to a few LFB ships that pose a medium sized threat, jump in, let them scramble their fighters and light up their engines, and then jump away before it can crush you. Do that for a week or two, run the monster out of food and gas, and pretty soon it will have to either go home, or resupply on the road, in which case you could potentially use that as a moment to strike.
Honestly, only above the small number of targets that simply must be defended does one really need to think about fighting the thing. Sure you can't run from a place like Luthien or Terra or Hesperus or New Avalon or some place like that, and you can bet it won't retreat from Alshain or Rasalhague (and there it will have access to supplies). If you're in that situation, then you use what you've got, which is more likely to be vast swarms of fighters (no need to special infrastructure, and once the mission is over they can be dispersed into ten or twenty groups) unless you're the Ravens or FWL before the Jihad or one or two other groups. But, if you've got several ships to fight the one Leviathan, may as well just attack several other targets, and tie it up, and make it either sit over a place you're not going to attack anyway, or else chase you around aimlessly.