To challenge other fighters in the Liteboxer app, you'll first need to complete a Punch Track, Trainer Class or Sparring Session to challenge others to beat your score. You'll be able to see the leaderboard before you begin your workout.
After your complete your workout, click on "Create a Match" on your workout results page, and select another fighter to send your challenge to by clicking the icon to the right of their name. Then just tap "Send 1 Match" at the bottom of your app screen to send your challenge!
To see your active and completed challenges, simply toggle to the "Challenges" screen.