A quick query.

So I took a few million sats on the cheap out of the hands of the panic seller (thanks btw) and withdrew to my ledger nano x. When I clicked withdraw I got the option to move it over the main chain or via lighting but I've always done it on the first layer. I'd appreciate it if anyone could let me know if you can move BTC to cold storage via lighting, I feel like the answer would be no beacuse of the open channels but it would be nice to reduce fees when I'm self custody my bitcoin.

Thanks for any info and enjoy the cheap sats.