The LNAs of today have a given voltage range that keeps them within the class of operation design. If you go out of the voltage range. The amplifier will no longer be operating in designed classification. Then you will run into the above mentioned problems.
Running an amp at full output then attenuation is not the way to go. When building amplifier stages such as between the antenna and the first stage or between distribution points no mater if they are between multi distribution runs, filters or different or any other stage. It is best to keep the gain at 0 and never more than 1 or 2 Db.
This rule of thumb is used in all forms of analog signal processing. The only exception might be to add a bit of gain in the final stages to overcome poor ADC sensitivity.
Joe