He didn't lie. He just didn't tell the whole truth.
Now, some would say a half-truth is as good as a lie. I'm guessing those people would also think the justice system usually works to serve justice, rather than expediency. It turns out that half-truths make up a lion's share of tact. When you need to communicate something but don't feel you have the right to be blunt, or when the person you're talking about is in the room with you, or when you need to communicate something related to another thing, but that other thing is potentially private information you don't think you should share.
Claire might be one of those people. She's shown that trait when it comes to the sanctity of libraries. I don't see that as a sensible lead-in to a continuing issue, though. Maybe 1 or 2 gag strips, but Claire has also shown that once she's had a chance to say her piece, she is willing to hear the other side. She may not agree, but she doesn't seem to hold grudges.
As I see it, it all on Marten. Claire was hurt. Whether it was reasonable for her to be hurt is up for grabs, but it is, IMO, a mistake to try and make "reasonable" and "emotion" work like chocolate and peanut butter. Or Chocolate and bacon. Or Austrian accented Austrailian English.
It's not that the two are polar opposites, much like the examples that followed. They are highly interrelated, in fact. Emotion is all the feels. Reason is, fundamentally, when you're willing to be critical of your feels. 99 times in 100, we don't have the will for that, even when we think we do.
But Claire is pretty easy to mollify, and Marten knows this. Just acknowledging her feels would probably be enough, and it doesn't cost much. Zen Marten can do that, no issue. Passive aggressive Marten can't. While he was cool with Faye, it was pretty clear that passive aggressive Marten was in the house. What we don't know is if that was because it served the gag of the day, or if it was plot. So, it all comes down to which Marten shows up if Claire shows up.