For what purpose? I don't think it's needed if you are thinking it's needed for discussion & learning or even getting help. Because, you can learn everything here in the forum. A lot of legendary are here to help you and figure out if any problem you face to. I have recently had some discussion on Lightning Network and it's my pleasure that I have learnt a lot from the forum.
By the way, a beginners guide to learn basic about Lightning Network if anyone is interested- https://bt.irlbtc.com/view/5202798.0

Even though he missed the point, I still don't think it would make any sense. Lightning network has fees when you send something, pretty much like a transaction data, only messages this time. Another thing is that there are already a lot of applications dedicated solely for this purpose.

Another thing to point out is the decentralization that comes into play in Lightning Network. It would bring 2 main disadvantages; [1] It would make private data somehow insecure, since it is stored in individual nodes rather that governed under a centralized secured server, and [2] Even though Lightning Network is faster than the typical blockchain in terms of response time, centralized servers are still much faster generally in performance, which is essential in having an app with the purpose of communication.

Why not apply end to end encryption or PGP?

LN is not made for that purpose. Even if you want to do it, you'll need to open a channel here and there. Pretty sure end users wouldn't want to do that and just stick with whatsapp with a fake number.

send one word and my friend receive afer one block?

The problem I see is that users would have to pay to be able to chat (to open the channel) .

Also, once the channel is closed, messages would be lost, as far as I understand the lightning network. The messages wouldn't be on chain.

If you are thinking only about privacy, certainly there are better alternatives for a chat. Look for some Privacy friendly open source chat app here
Privacytools.io

There are many other "open source private messengers" (even p2p), that don't happen to require satoshis for sending messages. This idea is nonsense, it can be done from a theoretical point of view but its pointless and I wouldn't use it.

Take a look at the Tox protocol for better alternatives.

Whatsapp is one of the worst messengers you could possibly ever use.

You need satoshi to send messages, but you also get satoshi to receive messages. So people won't lose any satoshi on average.
Lightning wallet and chat software can be integrated into one app. I will use it. If they can support group chat in the future, it can be a game changer in social media.

But people get their privacy, think it as a kind of paid service for privacy.

I think there is a need to build a chat app on top of the lightning network.
Someone is doing this, check this out: https://twitter.com/joostjgr/status/1190714028626251779

There is a beta test already!

You should check it out.

https://sphinx.chat/

Someone on twitter asked something interesting: People could DDoS the lightning network with such a service. Need to think a way to prevent that.


There are even more interesting things that could happen inside such a platform. Merchants over the world could use that chat app to receive payments as well, not only messages.