Do I need to register VAT and Nexus for print-on-demand through Lulu Direct?

[ColorQuest]

I am a new Canadian Shopify seller. 

My products are physical books and ebooks.

All physical books are fulfilled by Lulu direct that has several printing centers internationally including USA and UK. 

Any order from UK will be fulfilled within UK and any order from USA will be fulfilled within USA through Lulu direct. 

I have no employees and have no warehouse or office in anywhere.

I am wondering if I need to register VAT in UK and Nexus (physical Nexus due to printing centers in USA) in USA. 

Can anyone have clear answer for these?