So, you liked this girl way back when, she never gave you any hints she felt the same-- so you went on vacation and hooked up with someone else.
I don't see the issue. You weren't together-- hell, you weren't even talking about DATING.
As for you "lying," when she asked if you hooked up with anyone-- that wasn't any of her business in the first place. It doesn't matter if you did or not.
As for her holding it against you now.. yeah, I don't understand that.
My guess? Her reason for not being in a relationship with you in the first pace is because she's "not ready," [even though she's basically in one] and now she has a new excuse that you "lied to her/she can't trust you."
Sounds like she's trying to cling to any reason not to be in an official relationship with you. It's time to ask WHY. -- Not only WHY she doesn't want to be with you officially, but WHY you are still pursuing someone who seems to only want the perks and not the title.