Counter LRM / Flak combo?

Yes.  HC is the answer in my mind.  Or a SB.  I've been partial to SBs lately.

if you are vasari you can go 100% assilents (not reccomended) and use them to take out the cap and lrms basically you ignore the flack until everything else is killed. if they get too much flack it doesnt work.

Recently I have found that you can use a fleet made up of 20 or so vasari scouts and tonnes of asilents and you need to mix flack in there if they get carriers. really scouts to take out lrms and cannon fodder if they want to waste their weapons on your scouts. you use the assilents and your egg to attack his cap. and dispite their flack i like to get fighters if you put them on hold position near their lrms they will take less dmg from flack and hopefully they move the flack to the fighters.

You can also attack with a fleet and build a SB at the same time and focus your fire on the lrms because flack do very little to SBs

advent you can spam illums but that isnt really a counter its just a display of how OP illums are.

Really the secret is to have a balanced fleet instead of a singe ship to counter it. you can even throw in lfs with their abilities if the TEC player gets hoshinkoes. (he probably wont attack your lfs with his lrms becase they are less of a threat, but micro your lfs around his lrms if he is attacking them their abilities are omnidirectional (i think) so you can take out his hoshinkoes and distract his lrms for a while.

If you're early enough in the game, flaks cannot completely counter fighters and scouts.  You do need to micromanage these units rather heavily, but it's quite feasible to wear down LRF by attrition.  If you can continually suppress the enemy LRF then you can bring in light frigates.  Remember, strike craft are way more mobile than any frigates, so any time a flak gets to fire a shot it's because you allowed it to.  Try to get the enemy to spread out and avoid letting them concentrate into a tight formation (easier said than done, unfortunately, but still doable).

Another alternative is to use hit-and-run strategies, falling back to a heavily defended stronghold if the enemy arrives in force.  LRF/flak comboes are very easily outmaneuvered, whereas strike craft can be in and out in a flash.  The tough part here is that you need strong sieging ability to threaten the enemy and prevent him from simply going around your defensive emplacement.

Heavy cruisers are the boring answer.  They won't work against Advent (repulse) and the Vasari ones are pretty unimpressive.  However, they will do the job otherwise.

Enormous amounts of Scouts are one of the best strategies against the LRF/Flaks, if only because of sheer numbers. However, this does take quite a few resources, and probably isn't viable for Vasari at all. The key is simply have the Scouts demolish LRFs, leaving the Flak intact. And they're easy pickings for LFs. Of course, this probably won't work if the Flak are in a formation to attack with all four guns.

Otherwise, Fighters actually do work if probably micromanaged, and are the fastest way to dispose of LRFs until the Heavies come out.

As Vasari, I should also add that getting a second egg is actually a great option.  Nanos is a death sentence to LRF, and two eggs constantly spewing this ability can actually counter a reasonable LRF force.  This enables you to focus the rest of your army on countering the other units.  Obviously this won't stop a critical mass of LRF, or against TEC with hoshis, but when it works it's extremely decisive.

Bombers. Resistant to flak and still deadly to lrms (not quite as much as fighters) The idea being however, you must take down the lrms numbers so you can get at the flak with lfs. Most likely your opponent will start building more flak to kill your bombers, thats when you dockem and send in the lfs to start shredding some flak. Its tricky but manageable. just make sure you use your bombers and your own lrfs to drop his lrf numbers. Additionally setting your bombers on hold position will keep them alive longer. Simply set them to hold position and then move (do not issue an attack order) close to what you want them to kill. 9 times out of ten theyll automatically attack their nearest target when they move to the position youve set for them. Also remember that LFs are faster than lrfs, if you can bait his lrfs out of the protection of his flaks by skirting the well with a group of lfs, you'll break up that nasty combo and your bombers/fighters will have free reign to blow those lrfs out of the sky. Once the  lrfs numbers are down, dock your bombers in the carriers to preserve squadron strength. When he realizes hes too low on lrfs to pummel your lfs he'll start rebuilding them. Thats when you launch again to keep em down while your lfs clean up the flak.

Best thing you can have in this situation is a balanced fleet. Get some bombers, flak, lrfs and lfs. Keep your bombers docked if their are any fighters in the area and use your own flak to thin them out before launching your bombers. Lrfs bombers and flak on his lrfs. Then charge in with the lfs.

If you can surmise that your nearest opponent is contructing lrfs and flak early, you can start building carriers early and loading them with bombers (the first 1 or 2 you build load with fighters so when he scouts you thats all he sees, and he'll feel delighted that hes already got you cornered with his flak) Then the rest go bombers and keep em docked. This way you can surprise him and maybe even be able to take out his Cap ship before he realizes his mistake. 8-9 squads of bombers will shred a low level cap with surprising speed. After a decent amount of carriers, go lrfs lfs and flak.