Lawyers (plural), not lawyer.
Why do they have to pay the plaintiff's lawyers? Because they won and Moore lost. This is a federal civil case and legal fees can be ordered paid by the losing side and there's a motion before the court for these fees. Because Moore was sued in his official capacity as Chief Justice of the Supreme Court of Alabama, not as an individual, the losing side is the state of Alabama, not Moore personally.
When the judge issued his order for fines when Moore refused to remove the monument, Moore would not be the one that paid the fines. Those fines would have to be paid by the state of Alabama becuase Moore was sued in his official capacity, not personally.