Congratulation on these LI amplifiers.
These are still superior to any digital FFT techniques in several cases.
At first, LI usually come with very sensitive and low-noise pre-amplifiers, combined with (selectable) high dynamic range, over 120dB.
They usually feature true differential amplifiers.
All this enables these instruments, to directly measure signals in the nV range out of many orders of magnitude higher noise.
This capability of LI still is far beyond FFT, as latter systems are dynamically limited, and also are difficult to be synchronized with the base frequency of the signal to be measured, so you easily get any kind of frequency leakage effects, or picket fence effects, which requires filtering, which again creates unwanted phase-shifts of sine and cosine components.
LI are much more straight forward in this sense. Also, with LIs, you can implement clever chopper techniques (e.g. optical) for dc signals, so to measure also these in the nV range with very high SNR.
FFT can be used better, if the signal is clean from the start, and if you are interested in the higher harmonics of the test signal, and you have the possibility, to synchronize the DUT signal with the FFT analyzer. Using LI amplifiers, you would have to stack them, each one for every frequency component.
Well, I have used and repaired a lot of P.A.R. LIs, especially many P.A.R. 124A.
Crucial components were the reed contacts, which switch the gain inside the ac amplifiers.
So I de-soldered these from their coils, and replaced them with modern reed contacts,. That way, even 25 year old LIs were like brand new, afterwards...
Wonderful electronics..
Frank