The one with the biggest amount of transactions is 2,945 tx on it, and tx are each 10 minutes. ~ 4.92 transactions/second.
Most exchanges are now batching transactions, and the average transaction has more than one input and output. Should those be counted as separate transactions, or do we count 100 addresses that receive Bitcoin in one txid as one transaction?
But I think he asks about the maximum possible, at which point LN renders the main chain irrelevant in capacity, so that limit might actually be triggered by the number of coins and funds available and the number of channels, the network could theoretically do 1 million TPS a second but there might never be enough participants do reach that.
I'd say there is no upper limit for LN. Transactions don't have to be public, so if the total network is doing 1 million transactions per second, anyone can send more transactions on their own channel.