LRFs counter cobalts, and counter them hard...pre-rebellion, it is probably the hardest counter in the game other than flak vs. fighters....
Either you are vastly outnumbered or you are being vastly outplayed....pure LRF should beat a comparable fleet made of LRF and LFs...if you are Advent and using illuminators, you must absolutely micro your units so that all three beams on each ship are firing...that means moving your illuminators into the middle of the fight...
You also need to make use of your Advent capital ships...malice on the progenitor and vertigo on the rapture are your friends (prog is a better cap to lead with)...these will help your ships outperform the enemy...
Remember that LRMs will beat illuminators in a straight fight unless you have cap abilities and really good micromanagement...
If you are getting to the late game, honestly you could just use heavy cruisers...of course the problem with that is bomber spam rapes HCs, but sometimes you can gain the necessary momentum with HCs to prevent an opponent from getting to that stage...