So, I've been watching and enjoying season 4 so far and just finished watching episode 4 a couple days ago with my parents. One thing I've noticed about the women's team so far is that we do not yet know who the captain is and I think its going to Lizzie.
From day one, when we first met Lizzie at the tryouts, what first impressed the coaches was her ability to deal with the constantly bickering twins Niamh and Siobhan. It felt kind of remenicent of when Isaac in 1x7 when he nudges his teammate to get off his phone while they're watching Iron Giant and Roy notices and it sets up Roy's eventual passing of the torch in matters of leadership.
Later in episode 4, when the cliques are arguing, Lizzie tries to sort everyone out she tries to mediate and validate everyone's feelings then when Gemma starts mouthing off Lizzie stands her ground and tries to put Gemma in her place. This demonstrates that she is willing to use both stick and carrot = willing to listen but not willing to be pushed around.
At the trivia night, when her team couldn't think of a name, Lizzie was giving all her teammates a fair go and trying to get them to vote and then takes charge when faced with their indisivness.
But what really made me think Lizzie was going to be the Captain was when Ted told the lady greyhounds that they were going to run back to Maeve's and help clean up. Lizzie wasn't happy either at first, but she was the first one to speak up and lead the pack.
The corolations between Lizzie being a mum and how she treats her teammates when they act like kids is a bit of a running joke but it also speak to the nature of how Lizzie's skills as a mother can be applied in a way that helps the team.
The fact that she's a little older and thus more experienced in life than most of the Greyhounds gives her a season 1 Roy vibe but not one that focuses entirely on drill sergeant leadership.
So that is my theory on why Lizzie will be the captain of the Greyhounds.