In Lyddie, who is the antagonist?

The antagonist is Mr. Marsden because he leered at Lyddie, forced himself on her, and got her fired.

An antagonist is an enemy, or the opposing force a character faces.  Lyddie’s first antagonist is probably Mrs. Cutler, because she is a horrible boss.  However, she is not at Cutler’s Tavern very long.  Although Mrs. Cutler makes life miserable for Lyddie and then fires her for leaving even though she had permission from the cook, she moved on from that experience.  Unfortunately, she found herself facing an even worse boss at the factory.

The factory system was very oppressive to begin with.  The girls had to live in the boarding house and do what the company told them, including dress a certain way and attend church.  Lyddie’s boss at the factory was a leering, completely inappropriate man.  When she was sick he forced himself on her when she couldn’t defend herself, trying to kiss her almost before she realized what was happening.

She tried to stare him down, but her eyes were burning in their sockets. Let me go! She wanted to cry. She tried to pull back from him, but he clutched tighter. He was bringing his strange little mouth closer and closer to her fiery face. (Ch. 16) 

Lyddie stomps him and stumbles away.  After this she is in a fever for several days, and nothing comes of the incident.  By the time she returns to work it is forgotten.  However, she still feels uncomfortable around him because of the way he stares at her. 

One day she sees Mr. Marsden and her friend Brigid.  He is trying to do the same thing to her.  Lyddie does not think.  She just hits him with a bucket. 

At the sound of her hoarse cry, the overseer whirled about.  She crammed the fire bucket down over his shiny pate, his bulging eyes, his rosebud mouth fixed in a perfect little O. The stagnant water sloshed over his shoulders and ran down his trousers. (Ch. 20) 

This time Lyddie is fired, and she accepts this.  He accuses her of being immoral, which is ironic since he is definitely the immoral once.  However, she does write a letter to Mr. Marsden’s wife exposing him and gives it to Brigid.  She tells her she must promise to give it to his wife if he targets her again.  It is the best she can do to protect her and the other girls from this predator.

Who is the antagonist in the story "Lyddie"?

If you are looking for the (single) antagonist of the story Lyddie, I think you have to go with Lyddie herself. The bank, the bear, Mr. Mardsen are all good choices for antagonists. They are antagonists. But the main antagonist I still think is Lyddie. Or at least her attitude regarding money.  

Gaining financial independence is all consuming to Lyddie. She is farmed out to work at the tavern in order to help pay off family debts, but she feels equivalent to a slave. Working at the textile mills offers her a chance to make more money and make it faster. That way she can pay off the debt and no longer be financially in debt to anybody. Lyddie also wants to be financially independent enough to not have to depend on anybody except herself.  

This single minded focus of hers is admirable, but it ultimately hurts those around her. For example, at one point in the story Lyddie is asked to teach a new Irish worker how to work the looms. Lyddie is so frustrated by the end of the day at how much her own work is being slowed that she tells the boss to give the new worker her own machine. That would be okay if Lyddie was confident that the new worker could work the machine, but Lyddie knew full well that the worker wasn't ready and was likely to get hurt. Lyddie's focus on herself and her ability to earn money put someone else at risk. It's not until the end of the story that Lyddie changes her main focus and decides that the best way to improve herself is by getting an education.