Set the WinnerId SyncProperty to the player who completed the laps first

GameSceneManager.cs

void OnTriggerEnter(Collider other)
{
    GameObject go = other.gameObject;
    NetworkID networkID = go.GetComponent<NetworkID>();

    // check if the player is the local player
    if (networkID.IsMine)
    {
        lap_ = lap_ + 1;
        guiManager.SetLapRecord(lap_, lapsToWin);

        if (lap_ == lapsToWin)
        {
            Debug.Log("Winner!!");
            string winnerId = remotePropertyAgent.GetPropertyWithName(WIINER_ID).GetStringValue();
            Debug.Log("OnTriggerEnter winnerID " + winnerId);

            // if winnerId is empty, local player is the winner
            // If the winner did not leave the game and finished the laps again, the player should still be the winner
            if (string.IsNullOrEmpty(winnerId) || winnerId.Equals(NetworkClient.Instance.PlayerId))
            {
                remotePropertyAgent.Modify(WIINER_ID, NetworkClient.Instance.PlayerId);
                guiManager.SetMainText("1st");
            }
            else
            {
                guiManager.SetMainText("2nd");
            }
        }
    }
}