How to set up a participant lookup page available to public?

From your dashboard, go to: configuration -> advanced config -> configuration section: 

1- Click edit, then enable on the 'registrant search page config' to activate the page

2- Click on "edit" next to the enable to set up the display of the page: 

3- The lookup page button is then available from the event/club landing page: 

Click on "view registration page" : 

Pages will look like below, and are accessible from all types of device: