First of all, welcome to the list.
Noise performance of both a traditional mic pre like an API circuit and the newer CFIA circuits found in pro-sumer mixers is better at higher gain. This is because, as explained in the
Designing Mic Preamps presentation from THAT Corporation and as summarized in the plot of EIN vs gain:
View attachment 86149
, all else being equal, EIN of the pre will depend on the thermal noise of Rg and because Rg in these amps gets smaller as the gain goes up (Rg is the gain control pot in a an API style pre), thermal noise contribution decreases and therefore so does noise.
This plot also shows that the performance of CFIA at low gain is very good compared to the others. So noise is
not better at lower gain. I don't know what the EIN of the cloud lifter circuit is but if you added that data point to the plot, it would be well above the others. It wouldn't even be close.
So regardless of the pre topology, you will get superior noise performance from one single high gain stage. Adding the cloud lifter can only decrease noise performance.
If you are experiencing otherwise, then there could very well be an issue with the environment around your pres or the pres themselves and the cloud lifter is helping because it's floating in a balanced line so it is not contributing common mode noise. Laying out gear and cables and minimizing EMI requires a lot more knowledge and care than most people think. All sorts of problems can occur that generate noise and hum. My MOTU Traveler mk3 makes a whistling noise at ~2kHz when phantom power is on presumably because of the 48V SMPS.