I would turn off all of the circuits in the house (all of them) except one 120V receptacle circuit, then plug in a hair dryer or heat gun or space heater, something with a reasonably significant load.
Check the voltage L1-N, L2-N, L1-L2 with nothing operating. Then turn on the heat gun (and nothing else) and check the voltages again. One line will have the load and the other line will not.
If the voltage goes up on one line to neutral and down on the other line to neutral and stays about the same on line to line, then this is an indication that there is a high resistance connection in the neutral feeding the panel (typically a PoCo neutral connection, but could be a meterbase issue but doubtful).
Don't let the PoCo rep just say everything is fine. Years ago I stepped outside and saw that there was a PoCo service truck next door. Being the curious fellow I am, I asked what was going on. I was told about flickering lights and watched the PoCo tech use a meter to check voltages and said everything was fine, and started to leave. Neighbors looked lost.
I intervened and did the test I described above and showed the PoCo tech that the voltage went up on one line and down on the other and that they indeed did have a neutral problem and he should not be leaving because they have a problem (I was pretty adamant to him). He went to the radio for a few, then came back with the "beast". Plugged it in, read the data, called in for a digging crew that found the underground splice that was defective.
