You'll need a really sophisticated meter to measure the instantaneous LRD. None of mine have been capable but a really good Fluke or HP may.
My experience: I run a small dorm fridge, average running draw is a bit over 80W. A new Samlex 600W inverter was unable to supply the LRA draw. I replaced the Samlex with a Xantrex 1000W inverter and all is now good. I'd estimate the LRD to be around 6-8 amps @120V. I had both inverters wired to two battery banks with a minimum of 4 AWG from 18" to the battery location.