When did you first ask her about the last time that she slept with fuck buddy? Was it before you mutually decided to be exclusive, as in: "are you currently sleeping with any one else? have you slept with any one else recently?" Or was it after you became exclusive, as in: "when did you last sleep with that guy, before we became exclusive?"

She shouldn't have lied to you. If it was the first situation, and you were asking about her current or recent sexual history because it might affect your decision to become exclusive or not, the lie is more concerning to me. I think it's fair and reasonable to ask sexual partners if they're currently sleeping with anyone else. If it was the second situation, and you were retroactively prying into her sexual history, it was still unethical for her to lie to you, but it was also none of your business and not "in bad taste" for her to exercise her sexual autonomy in whatever way she wanted before making a monogamous commitment to you. I suspect that she might have lied because she knew you would negatively judge her or because she didn't expect you to react well if she said it was none of your business. In that sense, I think you both let each other down.

I can understand you feeling hurt by the lie. If I was in your position, I would try to focus on how she's behaved since she made her commitment to you. Has she been a kind, respectful, and reliable partner? Is the lie part of a larger pattern of self-serving dishonesty, or has she given you no other reason to doubt her faithfulness or honesty?