Could anyone tell me if there any airlines flying between Lax and Vancouver - not pulled up on Expedia.co.uk - i.e. low cost airlines such as RyanAir in the UK

Unfortunately, Alaska Airlines controls a lot of the west coast and their fares are not at all low cost. I think United may fly that route and they have a low-cost alternative called "Ted" now - you could check that. Good luck.

HMY Airways is sometimes low-cost, but often Alaska Air is comparable.
http://www.hmyairways.com/

You can get direct flights with a number of airlines - try America West, Northwest Airlines, Alaska Airlines as mentioned above and Air Canada. You should be able to find flights for as little as $400 return or with Air Canada's affiliate "Tango" about $180 one way. Doing a yahoo or google search should get you to the respective airlines web pages.

I would like to clarify the comment made in the previous post about Tango. Tango is not an affilate of Air Canada but is simply Air Canada's lowest fare class. These fares tend to sell early. I don't know if expedia shows Tango fares. Try aircanada.ca

I stand to be corrected but my understanding is that Tango flights are separate planes, not just a different fare arrangements on an Air Canada flight. Maybe it is different transborder?

Tango used to be separate planes with a one class configuration and different paint job. Now Tango is a fare class available on domestic and transborder service using the same planes that people paying more fly in. There are still planes painted in the Tango colour out there but AC abandoned the idea of running a separate discount airline and incorporated some of the Tango features on the mainline fleet.