That depends whether we're talking about on-chain/off-chain and use SegWit/not. If we're only talking about tx/s on-chain, then it would be :
1. about 7 tx/s if all transaction don't use SegWit
2. between 12-20 tx/s if all transaction use SegWit

But if we're talking about off-chain tx/s, then in theory it's unlimited (ignoring on-chain transaction to open and close channel)