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If you contact BGL via E-mail or phone, expect typical crap replies - "we don't work with offshore/non-resident/non-luxembourgish"; "we don't share this kind of information due to internal policy, bla bla bla...". You have to go in person to hear anything useful in regards to account opening. Having an EU VAT number should do the trick, even if EU sales are a tiny percentage of your turnover.
This is the response I got for Malta company: "To open a business account in our bank, the company must establish (office and activity) in the Grand Duchy of Luxembourg or there must be a direct link with the Grand-Duchy."

Well, I normally don't mind going somewhere if the bank wants to meet me in person, but they at least have to show some interest and put me through to a right person, who will do some preliminary assessment.