Thank you for your quick replies. It's clear for me now that I can freely transact through the Bitcoin Lightning Network being an EU citizen.
This is unrelated to the question but anyways:
Are there any ways I can buy Bitcoin and withdraw it into a LN wallet/address directly?
(avoiding the transaction fees two times between CEX -> wallet -> LN and then back to LN -> wallet -> CEX)
I have been navigating several DEX but unfortunately I couldn't find any that would transact in the Lightning network.
As far as I know for the time being only financial institutions in EU are prohibited from using XMR, DASH and other privacy coins. Individual users are still allowed to use them as long as they are not transacting with the financial institutions.
However EU is trying to phase out cash indeed. The EU governments are gradually lowering the maximum allowed limit of cash transactions. It varies from country to country but in most cases is somewhere in the range from 1,000 EUR to 5,000 EUR. However these limits are constantly being lowered. For example in Greece they will soon limit the max. cash transaction to 500 EUR.
If financial institutions, which include CEX, are prohibited from using XMR, DASH or transacting in the LN.
How is an individual supposed to access these crypto assets? (open question - I'm not currently looking forward to acquire any of these - curious about the legal aspect)
I can buy a beer with LN, so no, it's not banned.
Don't trust Binance, they'll try to trick you into accepting their own made up tokens instead of Bitcoin. They have no interest in letting you withdraw real Bitcoin.
Thanks for your comment - I'm glad you can buy beer with LN
For now, Binance is my main CEX (in the past I've also used Coinbase) - looking forward to learn more about the alternatives