Hi, Welcome to OpenStreetMap.

I can see nothing here that is mapped/tagged as LN2 2ZE, therefore there is nothing wrong with OSM data.  

I did investigate and found as you might have that Royal Mails postcode finder is incorrect. In that it wrongly shows LN2 2ZE in Nettleham. It is Royal Mails postcode positioning software that is at fault. You could try contacting them.

I've removed the fixme.

Regards Bernard.