Yes. You can do that with Blixt, Zeus, Phoenix, Mutiny and Breez. Read more about these mobile private LN nodes here
The procedure is simple, when you hit the "receive" button, you will get a wrapped LN invoice from the LSP. Somebody else or you can pay that invoice from any other LN wallet with funds and in few minutes you will get your first LN channel opened from the LSP towards your mobile node, with the funds you deposited pushed on your channels side.
Remember that this procedure imply some fees necessary to open that LN channel towards you. But this is only first time the channel is open. Once you start spending from that channel and "you make more space" to receive, you will not be charged anymore that opening fee. That's why is recommended that first time you open a channel, open a bigger one (2-3-5 M sats for example) to have more space in the future. These channels you can refill them anytime with a submarine swap, without closing and opening new ones.
Thanks for you information.
Basically, if I'm using Zeus, Phoenix etc with their LSP and I don't own any sats and I just have an empty wallet, I need to receive as first payment via Lightning at least 30-50k sats (amount is up to the wallet) in order for the wallet to receive the payment and be able to open a channel, correct?
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Yes. Once the channel is open you are ready to spend those sats over LN. I would recommend to open your first channels slightly bigger. I consider 50k sat channel too small and you end up paying more fees in the end.
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