There are a few questions mixed in here:
Does Leanpub collect and remit VAT on its sales?
How does Leanpub pay royalties?
Are there VAT concerns with royalties?
In terms of the answers to those:
Leanpub collects VAT on purchases and remits through VAT MOSS. Details here: http://help.leanpub.com/reader-help/why-do-book-prices-have-vat-added
We pay royalties monthly, with a 45-day hold on the royalties from each purchase (because of refunds). Details here: http://help.leanpub.com/author-help/selling-and-royalties/how-and-when-do-you-pay-royalties
We don't provide tax advice, but royalties are royalties, and we do not charge or remit VAT on royalties. You do not need to send us invoices. Details here: http://help.leanpub.com/author-help/i-have-a-business-and-my-accountant-says-that-i-need-to-collect-and-remit-vat-on-my-ebook-sales