How many paths are tried on average before a payment succeeds in Lightning?
I don't think there is a Public dataset online with an answer to your question. This would also be extremely hard to create as the results could change a lot depending on which node is doing the experiment.

I know people are probing payment channels you could do the same. Just do payments to random payment hashes and collect the data for your node. You will get the routing failures and attempted tries in that way you can easily collect those statistics yourself.