I lied to my girls and lost there trust

[XxDog8]

Hi
panic moment - I spilt up with the kids dad last year and kids stayed with me - not much contact with their dad.
I have formed a friendship- nothing more- with a colleague met through work (never met as works on another site) - been chatting for a few months now by text and kids know about this.
we decided to meet last week just for a face to a message and innocent dog walk. Problem is I lied and said I was meeting a girlfriend to the kids.
my youngest has found out and carried the burden up until today telling no one - she’s been off with me all weekend and now I know why.
I have confronted her and apologised for lying and explained I just couldn’t be bothered with the hassle …. She didn’t want to know and basically said ‘why lie then’ - which she is right about.
Now feel sick I have destroyed all trust in me after the hard decisions made over the last year to leave their dad.
I have no romantic intentions to my colleague- it’s just companionship when I am on my own- someone to text is all.
how do I get my DD to trust and understand why I lied?
any advice would be helpful

How old is this girl?

You can't, really. You can only not lie to them going forward and hope they begin to trust you again eventually.

Why did you lie? Figure that out properly, be honest with yourself and then present that to her in an approach way.

Apologise,admit you fucked up, and adults do do that sometimes and tell her that while you understand that you broke her trust, you will be working to show her she can trust you and you'll be honest with her from now on.