What is the power consumption of my LG refrigerator?
The nameplate wattage is volts X amps, or 127V X 2.4A = 305 watts. That's what the fridge will draw when the compressor is running. The compressor only runs periodically (ballpark 25% of the time, depending on the model), so the long-term average will be quite lower.

However you should also be aware that all motors, including the one in a fridge compressor, draw significantly power power during the first few seconds of operation. Could easily be 3 times as high. So if you are going to be running this from an inverter, make sure it is capable of around 1000 watts. Sometimes inverters have two ratings, a "surge" rating and a "continuous" rating, for exactly this reason. However the exact definition of a "surge" rating on an inverter is ambiguous, and some of them are only capable of running at their surge value for a fraction of a second, which may not be long enough to get the fridge started.

You haven't posted many specifics about the inverter or microwave, but running both appliances from that inverter may be pushing it, especially if the fridge compressor comes on when the microwave is going. Microwaves can draw 1000–2000 watts or more. (The "wattage" rating of a microwave is the energy that the food gets... actual consumption will be higher because of energy loss, electronics, motors, lights, etc.)