Bar tab is so very bad analogy here that breaks for multiple reasons:

- At the bar is almost always a single direction: customer pays the bar. Lightning is both directions - sending money between friends and sometimes to shops.

- In this (bad) analogy bitcoin would not be Visa, but bitcoin would be "dollars". Both the bartender and customer would say that they are using dollars for the tab.

- The tab analogy doesn't really match the fact that you establish a "channel" (e.g. both you and the bartender would put some bitcoin into this channel and then you can pay your grandmother in another country with bitcoin in this channel... see the analogy doesn't work here), you can resize ("splice") the channel if you want, you can swap in and swap out...

In most solutions your wallet monitors the chain and it automatically resolves any of the dispute (e.g. Phoenix wallet, or Zeus). The time scale is also different, so even if power goes out for multiple days and you are running your own very private wallet without any associated service (LSP), then you still have on the order of weeks for your wallet to automatically resolve any issue.