To open the sign up page in Lock you can use the [initialScreen] (Lock Configuration Options) configuration option. To send values into the hosted login page, you can send a query string parameter. In your application you would send:
webAuth.authorize({
mode: 'signUp'
});
In the hosted login page, you’ll then just need to add the initialScreen attribute in the Auth0Lock initialization code as:
var lock = new Auth0Lock(config.clientID, config.auth0Domain, {
(...)
initialScreen: config.extraParams.mode,
(...)
});
edit: removed 404 link