An effective and cheap counter to an LRM Carrier is a J. Edgar or Harasser. Spam a few SRMs and immobilize it with minimal risk in return due to speed and (hopefully) minimum range modifiers. That doesn't work nearly as well against CLRMs, due to the lack of a minimum range penalty. A Locust or Mercury does well against LRM Carriers as well, and if the opponent places a bodyguard tank, just wait until you win initiative, run in, and stand on the bodyguard tank while you shoot at the LRM Carriers. Stomp during the physical phase, hopefully killing two stones with one bird (or bug), or something like that.
LRM vehicles work well as supporting elements of a larger force, not so well on their own. Having them rain LRMs on the enemy while your own 'Mechs hold the enemy in place is the ideal. The vehicles can usually deliver more firepower per ton or BV than a 'Mech, but won't hold up as well under fire, so using them as support (IDF or otherwise) utilizes their strengths while minimizing their weaknesses. It doesn't seem to me like infantry would be an effective way to pin the enemy in place for long enough to make it work.