To enter Main Lobby you need at least 1000 points and a karma of AT LEAST -5. Then you can buy the main lobby ticket and gain access. Competitive lobby is similar except you need at least 2500 or 2000 points and a karma of at least 0.
The ticket button is on the very right hand side of the lobby tabs (right next to Sandbox Lobby there is a little grey ticket icon). Click there to view available tickets.