Hi John - and welcome to the forum. The website that Bart has pointed you to will definitely help.
You are entitled to live and work here legally as a member of the EU - but you will need to register for an NIE number when you arrive (tax purposes). The Police Station in Arrecife ties it all in with doing Residencia now - so two birds with one stone and all that. Have a look on Lanzarote Relocation, and all the info you need to apply for Residencia is in there hon.
Regarding setting up a business - definitely speak to an expert before you do anything - as it will save you a fortune in the long run and protect your interests. We always recommend Phil at
www.lanzabusiness.com - he posts in this forum quite often too, so may well say hello to you himself.
Definitely save up your money... as gaining a good reputation in a new business can take a little time. Also - if you can learn Spanish in the meantime, that will definitely help - especially if you are planning to move in with your new girlie in the North.
Good Luck!
Elle
PS: I went to Bangor once as a youngster - about 30 years ago LOL