I remember someone like achow, nullius or theymos saying that right now, you need that both parties are online, otherwise it wouldn't work, which is a big fail and will never get anywhere when it comes to mainstream adoption, but then again, I heard that they are working in ways to mitigate this and avoid needing to have both parties online at the time of the payment which is just ridiculous, it will never catch up, people don't like that, they will most likely resort to third party stuff which will come with a decrease in privacy unfortunately. I wish there was a way to leave the transacion "on hold" until the other peer connected or something.
You're missing the point.
The Lightning Network is a layer on the bitcoin blockchain; it does not have the infrastructure that the underlying blockchain does.
In bitcoin, the recipient of a UTXO does not need to be online because there are other people doing that job: nodes.
Nodes track UTXOs and store unconfirmed transactions in their mempool.
The Lightning Network is just a layer, it does not have nodes.
Even though bitcoin transactions are technically peer-to-peer, the nodes act as
facilitators to Every transaction and UTXO.
The Lightning Network, however, is strictly peer-to-peer.
Transactions between peers in a LN channel are just signed bitcoin transactions that aren't broadcast to the bitcoin blockchain, so they are sent DIRECTLY between themselves, without need for nodes or miners.
If Alice is sending bitcoins to Bob, Bob doesn't need to be online to track or receive the transaction because other nodes do the work because Alice's bitcoin node BROADCASTS the transaction to the other nodes in the blockchain.
If Alice and Bob are peers in a channel, and Alice sends some funds to Bob in form of a commitment transaction, it will fail because Alice is sending the transaction DIRECTLY to Bob's node, not broadcasting it, and if his node is not there to sign the transaction too, then it will fail.
There are no other nodes involved in the transaction so there is no mempool for transactions to reside till the other peer comes online.
Also, commitment transactions are multisig bitcoin transactions (2-of-2 multisig p2wsh transactions to be precise) have to be signed by BOTH parties so if Bob is not online then he can't sign the transaction. A third party, Charlie, can't act in lieu of Bob, because that would require them having Bob's private key.
To summarise the reasons why payments fail when a counterparty is offline are:
1) transactions require the signature of both parties, and obviously won't work with just one signature
2) the transactions are relayed directly p2p, and there are no other nodes that are involved to store transactions