VAT on goods bought and sold inside EU

Hi, first post after using Quickfile for four years, got a VAT query I could not find the answer.

I’m selling packaging materials which are made in Lithuania (EU) to customers in the UK. One of them decided to move some manufacturing to EU and wants me to deliver new label shipment to his sub-contractor in Holland. How to correctly account for VAT as my goods won’t enter the UK, they will be shipped inside the EU from Lithuania to Holland directly?
Should I just simply mark my invoice as Out of Scope for UK VAT?
Could my Lithuanian supplier charge VAT at source because goods are not leaving the EU and I don’t have EU VAT number?
Thanks Ed

Is the customer VAT registered in the Netherlands?

This sounds like a case that would have been covered under the “triangulation” rules pre Brexit but you may find you need to register for VAT in the destination country yourself now…