Self custody wallets do not rely on LSPs to make transactions they rely on the liquidity of your node and specifically your outbound channels.

An LSP can help you out by opening a channel to you thus letting you receive larger payments but your outbound is specifically tied to how much you have tied up in channels going out to other nodes.

Dual-funded channels are changing that so you can open a channel and if both parties fund it bi-directionally then you have both inbound and outbound in one channel.

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Now a lot of wallets out there that act as self custody wallets do use their own LSP like Zeus and Phoenix, but it doesn't mean that a wallet that can be classified a self custody wallet relies on an LSP.

I thought that with, for example, Zeus, the model is:

1. You create a lightning channel between your phone's node and your LSP (zeus)

2. Because zeus is online 24/7 (and provides other services like an ln address w/ zeuspay) that this makes them a good place to open a channel with.

3. My inbound liquidity remains limited to whatever that channel has in it. When I first open the channel, it is 100% outbound liquidity.

If I move $50 into my zeus wallet from on-chain to lightning, it opens such a channel, then I have $50 in outbound liquidity, right? And no inbound liquidity? But couldn't I theoretically do that with any available routing node out there even if they're not an LSP? Aside from maybe missing out on some uptime and zeuspay, if there any difference?

So I haven't used Zeus's node in a phone, nor them as an LSP. So I'm not sure about the specifics, but either they are opening a dual-funded channel to you, or they are opening both an inbound and an outbound. If you look at your wallet / node's channel page and you only see one channel with both an in and outbound, it's probably a dual-funded channel.

Gotcha thanks for the help mate!

Other LSPs work differently. I know for instance, LNbig only offers inbound channels and you can purchase relatively large inbound channels for cheap.

ThPhoenix came out with something that looked pretty neat, but I haven't tested out. But I think it uses dual-funded channels as well.

I know you can rent inbound liquidity from phoenix and zeus, which I think is the same thing you're talking about. I just tested out making a new channel with a random lightning node. It works! Now I can route payments via zeus or this other random node, whichever is cheaper at the time. Bitcoin is fucking rad,