My LTR of a year has been messaging her ex. This is the second time I've caught her. TLDR available at the bottom.

Background info: LTR participates in a coed sport at a highly competitive level. Her ex of 5 years is on the same team as her. To paint a picture, he's the type of guy who'd fly across the country to see her in a heartbeat if she said that she missed him.

Our original agreement was for her to keep all communication with him platonic and only limited to their sport. I later found out that she continued to vent to him and he was willing to act as an emotional tampon. I called her out and she said she'd cut him off. Two months later, I catch her doing the same thing. She would text him and vent to him about random shit. I called her out and asked her what they talked about to see if she would be honest, but she lied and only said that she reached out to him for team related stuff and that she should've told me about it.

My theory is that she's insecure about me and is continuing to keep her ex around for all the emotional support shit because she's scared I'll leave her. She's aware that my girl friends are interested in me and don't make an effort to hide it. I also don't give her any of the emotional support shit that her ex does.

Overall, she's a pretty good girl in terms of looks, career, and support. She does everything I currently look for, except that she's a liar. I don't plan on marrying her, but would like to keep her around for my benefit (professional development - her network is amazing) and would like to demote her to a plate. How would you guys approach this?

TLDR: LTR lied to me about messaging her ex twice. I know for a fact that they didn't hook up, but I can't LTR someone who is a liar. How should I proceed from here if I would like to demote her to a plate? I've already told her that we're on break and I'm going to do as I please.

This is a huge concern for her as she knows that my ex is accessible to me at any given time. I'm also in a similar situation to her where I participate in a coed sport with my ex as my partner.