I know this car has traction control but does it come with stability control as standard? I'm thinking of getting one a couple of years old

Not as standard, as you say it comes with ASR but ESP is an option.

ESP was only standard on the Elegance 4x4 and was not available even as an option on the L&K, this is according to the brochure so it might not bee 100% accurate.

It's highly unlikely you will find an L&K with ESP so you'll have to settle for ASR.

I've seen one advertised as having ESP. If I go to look at one how will I know,will it have an ESP button on the dash?

Yep, either way it will have the button on the dash.