How does the number of cycles for averaging in a lock-in amplifier relate to low-pass filtering and where do I set it?

Please forgive me if I ask too many questions at once or I am too much of a rookie. I want to understand the working-principle of lock-in amplifiers (LIAs).

I understood the calculation that yields the outputs for X,Y,R and Φ. I am only interested in R (the root-mean-square amplitude of my original signal that was buried in noise).

But then I got bamboozled: In all these explanations on LIAs, it seems to be assumed that R is constant??? But R is not constant, my original signal can vary over time! When it is said that LIAs only measure AC and are not capable yet of DC signals, I am sure they refer to the modulation, not the original signal. But then I thought, that probably you would just average over a certain time period and this would give me a trade-off between signal response and noise cancellation.
–> Is this train of thought accurate ?

Also, where do I set the time span over which I want to average? Is this the bandwidth of the low-pass filter?

(Maybe too off-topic: Can someone tell me what DC offsets are in the context of LIA ?)

I would be really happy for responses and I hope I don’t get downvoted for asking non-expert questions…