Is it active mixer? I think increasing LO (till some point) gives more time of useful switching in waveform. And after low pass filtering of that waveform amplitude will be a little higher.
After a certain amount of LO power, the mixer is practically insensitive due to highly enough LO driving level has been obtained.
By increasing LO power for vaste, you will increase also LO leakage at the output that is so bad. So, keeping a sufficient LO power will be better for mixer.