During the quest, the OL can get hero tokens by killing them with a specific monster. In the Victory section, it says:

If a hero moves off the map through the Exit, the heroes win this encounter.

If the OL ever has a hero token from each hero in his play area, the OL wins this encounter.

The OL keeps 1 hero token he has gained from each hero in his play area for Encounter 2.

Does the OL have to win encounter 1 to keep the hero tokens?

No, he keeps tokens regardless of the winner. The more tokens he gets, the more times he can move the beacon.