So for instance

Quite a few split systems have a minimum compressor run time of say ,,, 3 mins. This is programed into the system control stratagy.

On older fixed speed compressor units that had no oil seperator at the outdoor unit the manufacturers opted to make a minimum compressor run time to ensure oil return as the oil had to go all the way arround the system & back to the compressor.

Unfortunately if the unit was oversized which is common for heating mode when the system has been selected for max cooling duty, then the unit could overshoot the set temp before completeing the min comp run time.
Ofcourse this is not an issue on larger VRF systems which have oil seperators which are 99% efficient. But manufacturers of budget split systems need to keep cost as low as possible so the compulsary min run time is an easy option rather than install oil seperator.
I did overcome this problem a few times by fitting a time delay relay to the compressor contractor.
The min compressor run time is based on the max allowable pipe lenght & so if you have short pipe lenght then you can risk a shorter min comp run time by fitting the time delay relay so the comp will only run for 2 mins instead of 3 mins.
Ofcourse this makes the warrantee invalid & you risk stuffing the compressor.

You might find that your unit will run the compressor for a fixed speed for a number of mins. At the end of this period the circuit board then looks at the return air temp & the indoor coil temp & makes a decision what to do next. If the temp is near to set point then it may ramp down the comp. But if its has already reached set temp or overshoot then it will stop the comp.
So in this part load situation the compressor never gets to ramp down.

I dont have detailed info on LG units control stratagy so this might or might not be whats happening on your system but it is something I have seen a number of times before on a number of different types of split system.

Unfortunately with inverter systems it would be difficult to overcome this unless the manufacturer has some dip switch or function setting options & with budget a/c kit thats not very likely.