Besides atomicity AMP idea has a useful property of single payment being split into a bunch of smaller transactions, because once divided a large payment has way better delivery chances.

Furthermore, atomicity itself is often not required and partially fulfilled payments are sometimes more preferable to atomic ones. For example, consider a case when someone refills a balance on a lightning-enabled site using non-atomic 5-part payment: even if only 1 part is successful that is still better than nothing at all.

Therefore, it makes sense to enable payments which can be broken into smaller parts but are not atomic. As of update 0.3–116 BLW supports such a scheme on TestNet and it works as follows:

When generating an LN invoice payee software embeds a special multipart LNURL tag which contains a callback URI. An effect of this is multipart-enabled wallets now recognize this possibility while other wallets just see a usual LN payment request. Wallet asks user permission to split a payment in case if sending it in one piece has failed or if no single channel has enough balance to handle it. Once accepted wallet calls an embedded URI and gets a JSON response which contains additional invoices, it then proceeds with spreading total payment amount across these invoices and fulfilling them one at a time.

My hope is that multipart/AIR/AMP combined with unbounded channels have a potential to solve current liquidity issues for good.