Do not beat the snot out of your fridge's compressor, just to do a load test on the batteries. The compressor will likely overheat and perhaps shut down, and then you would not be able to estimate how much it was indeed drawing from the battery bank, and estimations of its healthy without knowing that are near useless.
Use the inverter powering a 100 watt incandescent lightbulb or something, so at least a known load can somewhat accurately estimate how much the batteries can still deliver.
13.7v float is high for lifelines at 77F
I've found my Northstar AGM responds best after a deep cycle then a high amp recharge. Being held for days at the proper float voltage does not yield an Overnight or morning voltage as high as the day after a high amp recharge from the most depleted state. This is also accounting for battery temperature as high amp recharging from a depleted state heat it much more.
The high amp recharge results are so repeatable that when I notice voltage lower than expected, and know it has been a while since it got fed a lot of amps when well depleted, I will intentionally discharge below 50% so I can pump 40+ amps into it( 90Ah capacity) for 25+ minutes then hold absorption voltage as long as required, usually 6 more hours, but it can be longer depending on just how many partial state of charge cycles or low and slow solar only recharges to full it has been since the last high amp blast.
I've not cycled a Lifeline to know whether it seems to respond as favorably to a high amp recharge as the thin plate pure lead AGMS like Northstar and Odyssey, but I would not test a sleepy bank of batteries that have been sitting at float.
I'd drain them, recharge them at 20 Plus amps per 100Ah of capacity, then test them, and no way would I intentionally hammer my fridge compressor to do so by leaving the door open.
If you do not have an inverter, this 25$ will be much cheaper than replacing a failed fridge:
I despise ciggy plug connectorsUse it to power an incandescent light bulb or something of a known, and fairly steady wattage.