We know the number of channels, the bitcoin addresses related to each (something researchers and devs are working to eventually improve on).

A big node in the network can probably get a lot of info for you, I feel like there might even be a company that produces a report like this if memory serves, but I don't remember who that was.

Oh, actually because of multi-part payments, even that might be inaccurate unless you treat each part as a unique payment.

I think what is most interesting is if someone has details on number/rate of FAILED payments. Again, will be a sample of data and we don't know what percentage but we can guess.

BTW the tldr is I don't know. I was simply talking about the mechanics of why we can't know payments per second.