There are three ways to get Lottery Tickets:

Every six hours you receive a free Bronze Ticket (keep in mind that you have to enter the Lottery in order to start the countdown clock)
 
Tickets are part of Milestone Rewards, the higher the level the more valuable is the reward

You can buy them in Lottery section or on promotional banners
 
After cashing in 7 tickets, you also get a free Bronze Ticket