Sorry, I don’t know how to measure an LNA’s noise figure with just a spectrum analyzer. Involves coax lengths, etc. Once, I did measure a WiFi bi-directional amplifier’s LNA benefit to an 801.11 non-OFDM signal. The affordable LNA within the BDA was a negative benefit. These WiFi BDAs try to use an LNA to avoid a seriously unbalanced link (TX range far greater than RX range).
OFDM mode is a totally different issue than single carrier (among the 802.11 standards). It’s due to the high peak/average power ratio with OFDM - and that requires highly linear amplifiers, esp. the transmitting amplifier. Typical low cost amp has to back-off 6dB when going into OFDM modes. (seldom admitted to in WiFi marketing).
The LNA adds non-coherent noise - lots of it. It’s important in the receiver’s bandwidth, say 20MHz. So you could assess a fraction of that bandwidth in order to cope with the spectrum analyzer’s high noise floor. But I think special equipment is needed to truly get the noise figure. What really matters is the BER and FER for DSSS and OFDM modes at different SINRs, for a real system with an without the LNA. The LNA needs to be right at the antenna, not on the far end of coax.
In cellular base stations, and military and other special systems, there are some 1dB or so NF LNAs that do have benefit, but they use supercooled components are are very expensive.