Trying to explain LN in just a few lines, I'm not sure it is possible
I think I can do it in one sentence too, in laymen terms: lightning is a second layer solution which takes advantage of the Scripting language of Bitcoin and makes it possible to trustlessly transact off-chain as long as the peers (or their intermediary partners) share a funded multi-sig address. 
That seems more a definition than an explanation of how the network works. But yeah, you're absolutely right. However, trying to explain how it works in a few lines, I think it's practically impossible! I mean, in a way the common mortal can understand!
There is someone in the Lightning Network Experience thread trying to learn the basics of LN without doing pretty much any research. That's the feeling I have! He's hoping to understand how it works simply by people spoon-feeding all info! And I think I'm going to give up explaining too much more if I feel he's not making any effort on his own!