No, my default notebook is Personal (Web).sorry my bad , is the Lumia notebook set to default notebook ?
Thank you for your comments. But, I do not like the third-party app ~4 days ago I messed up my notebooks , resulting many duplicates , SkyDrive\phone all was mess , I tried to reset my notebooks by going into phone settings ->system->office->reset and I lost all my notes , will never use one note , I am happy with evernote
I go to OneNote Online on my PC browser (IE9), there is no Lumia notebook too.I found how to remove a book after creating it.......to completely to remove it permanently you have to go to ...www.onenote.com......document.....highlight the one you want to remove then delete....so it will disappear from the app after syncing..
I have done that from a computer not from the phone...although it should work from phone's browser