During my experiments, I made pretty good experiences with the built-in low-pass filter (RXLPF) that is located before the third amplifier stage and thus also before the ADC (see pages 5 and 6 in the LMS7002M datasheet). I didn’t test it in regard to strong commercial FM stations, but in regard to a 5W signal transmitted on 51 MHz transmitted in about 10 to 20m distance (while receiving only 600 kHz lower), the built-in filtering worked amazingly well, considering the size of the LimeSDR Mini (I had to adjust the RXNCO a bit to gain optimal results for such a little RX/TX shift).
However, if you operate the LimeSDR Mini on frequencies below 30 MHz, you need to increase this filter’s bandwidth as the analog mixer’s frequency cannot be set lower than 30 MHz. If the filter bandwidth is too low, the signal that you want to receive will be attenuated too. You should be able to tune to the 10m/11m bands and reduce the filter bandwidth a bit (such that the frequencies you want to receive are still in the passband). I could imagine that this could improve your signal noise ratio. This wont work, however, on the lower frequencies, as the filter bandwidth needs to be wider in order to not block out the signal you want to receive.
I also assume the LNA needs to be low enough when there are too strong signals on the RX input. The TIA amplification stage already includes part of the low-pass filtering (1st order low-pass filter, explained on page 6 of the datasheet) and the PGA amplification stage is located after the full 3rd order (1st order + 2nd order) low-pass filter.
So try to set the RX RF frequency to just above 30 MHz, set the RXLPF filter-bandwidth a bit higher than the double of the difference between the RF frequency and your desired frequency to be received, and set the digital mixer frequency (RXNCO) to the single (non-doubled) difference. Then play a bit with the gain settings, and perhaps this will increase your signal-to-noise ratio.