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Yes, you do need to have some Bitcoin in your Lightning channels in order to receive payments on the Lightning Network. However, you don't necessarily need to own Bitcoin outright - you could receive Bitcoin from someone else through a Lightning payment, and then use that Bitcoin to open Lightning channels. Additionally, there are some services and applications that allow you to receive inbound liquidity through routing fees, but these can be less reliable and may come with some risks.

How could you receive a lightning payment in a sovereign way if you don't have inbound liquidity? Or without a channel previously set up?