Is this broadband noise calculation correct?
The sq.rt.(BW) ratio determines the SNR after the (LNA) low noise amp. Thus in order to achieve a minimum SNR for low jitter, you may need 15 to 20 dB or more (!) .
This is how to determine the required BW of the lock-in amp. Usually it is done with a much more stable VCO or VCXO or VC-OCXO according to the expected drift of the input f and tuning range of the PLL oscillator.
The other requirement may be to have a prefilter to prevent saturation after the LNA with more high gain of the next stages.
The BW of the prefilter can also be calculated by your formula to prevent saturation of the peak noise converted from RMS using a known constant (which I forgot at the moment). There may also be external noise not mentioned that must be prefiltered  and is likely much more significant than the LNA noise figure .