What did you mean by summary transaction? If you are referring to closing a channel, that's fine. As I and others have told earlier, when we close a channel, there will be an on-chain transaction. But all the other transactions happening between opening and closing a channel won't have any record in the Bitcoin blockchain. Imagine, you have opened a channel with 1 mBTC and spent 0.5 mBTC, you also received 0.2 mBTC. At this point, you want to close the channel. Your settled amount will be 1-0.5+0.2 = 0.7 mBTC. You will get this 0.7 mBTC on your Bitcoin wallet when a channel is closed and only this transaction will have a record on the Bitcoin blockchain.