In small numbers, lums are quite vulnerable to corvettes, but when the numbers are sufficient the corvettes don't counter very well...what is best to use as your counter depends on your faction and on whether the limiting factor at the time is resources or construction time....if you are Vasari and it is construction time, you are better off with kanraks...if you are TEC and it is resources, you are better off with corvettes...that's at least in perfect fleet vs. fleet scenarios....
You are actually better off not building any vettes if you opponent starts building illums, because by that point it is highly likely he still possesses a sizable force of disciples. Since light frigate soft counters vettes, your corvette force will be utterly crushed by that and malice. As for Vasari, don't build kanraks. They are the worst lrm in the game and if your opponent even builds a handful of vettes you are screwed. Instead, building a starbase is superior because illums are terrible at focus firing, effectively cutting their dps by half.
In reality, the Vasari player is probably coupling Orkies with light support (usually corvettes, flak, or fighters) and so you aren't going to get a true fleet battle...furthermore, Advent probably aren't going to build lums to deal with Vasari anyway since the Orkies force LF spam and carriers...for TEC, you will get a true fleet battle but by the time lums roll out, the limiting factor will likely be construction time, not resources so corvettes lose their advantage...unfortunately, the relatively long build time of LRMs puts them at a disadvantage as well...basically, no early game frigate is going to do well against lums once you get to decent fleet sizes (like 20+)...
TEC LRM grouped together in a tight ball will actually counter illums, because then they can't use their side beams. Its basically an imitation orky. And what is this nonsense about build time? Javelis has one of the best build time/supply cost ratios in the game in the game.
If the lums are coupled with malice, there really is no frigate counter as pretty much any ship (even HCs) will lose without heavily outnumbering the lums...I've faced a mid level prog and ~60 lums with my ~50 HCs and still lost -- the raw DPS of lums is insane and with large fleets + malice the weaker focus firing of lums is totally irrelevant for winning fleet battles...even Advent and Vasari minelayer tactics just utterly fail as the lums can instantly shoot in almost any direction (including behind)...
Again, if your squish all of your ships into a tight ball then the dps of advent is cut in half. People seem to think that you should spread your ships out when facing illums but that is a BAD idea. Also, illums dont have back beams. Are we playing the same game?
Your only true "counter" is fighters, and you better hope that your opponent didn't build any flak...I have actually beaten a slightly larger fleet of lums that had more tech upgrades by coupling my own lums with 3 aerias fitted with fighters....the thing is though, you have to hope your opponent didn't get flak, and if they start building flak then you are out of options...
Seleuceia two weeks ago- flak are shit
Seleuceia today- flak are absolutely overpowered
Conclusion- trolls gotta troll
The only way you are beating a decent prog with lum spam is with massive numerical superiority and/or some way to prevent the prog from using malice...usually TEC players have to get feed to do that, and have to have more factories since LRMs build slower per fleet supply...the only alternative is to build corvettes or LF and run your fleet, but that has its own risks...Vasari usually don't have this issue since Orkies encourage more LF spamming and use of carriers...
In short, once lum spam gets rolling you are screwed unless you have some other advantage already...it's kind of like missile barrage, you can deal with it but the best way is to never let them get it in the first place, and that's easier said than done...
I ran the numbers and lrm has one of the fastest build times per fleet supply in the entire TEC arsenal. You also seem to forget what you wrote two paragraphs ago, when you stated that flak can counter illums. You are completely correct on this point, because the fact that flak can fire in all directions (unlike illuminators) means that with sufficient micro, illums will take heavy losses. Add in the fact that illums do only 75% damage against flak, while flak does 100% damage, points toward the conclusion that flak is the go-to counter against illuminator spam.
Illuminator spam is also extremely unlikely in an equally skilled matchup without a feeder, due to the very high crystal and metal cost.