All three of the major resorst of Costa Teguise, Playa Blanca and Puerto del Carmen have a great selection of bars and clubs to visit but the latter is definately the place for late night clubbing.
Try the site
http://www.canaryislandsbarsclubs.co.uk and click on the island of Lanzarote it's a great site for finding bars and clubs across all the canary islands and has loads to view for Lanzarote you can even print money off vouchers and special offer vouchers for some of the bars.
Wherever you go have a fab time.