The site that you are referring to is not an official embassy site. Its a guide to all foreign embassies, and Google directs it to Libya, if that's what you have in the search bar. The 24 hour visa service is offered by a commercial company who apply on your behalf, for a price!! (And they cant guarantee 24 hrs) The genuine Libyan PB website is crap, out of date, and the only useful piece of info is their phone number, that you should call to check opening times, visa processing etc.