In 2018 the lightning network could do 15 transactions per second *per user.* (source: https://youtu.be/txcjxSRDvqQ) The phrase "per user" is important because that means there is no upper bound. If lightning has a million users then it can do 15 million transactions per second. This property, of scaling up with the number of users, is called linear scaling, and it's a whole 'nother league compared to bounded scaling, which is the type of scaling that centralized systems (such as Visa) can do. /1
Today, @grubles showed (https://twitter.com/notgrubles/status/1351031048046604288) that the 15 tps *per user* number from 2018 is higher now, and can be over 100,000 tps per user under optimized conditions (e.g. no network latency). Lightning gives that tps to *every user* -- consequently the network scales massively. More users = ever more tps.
Bitcoin Maston Instance