Is it ironic that...

So, I once worked at a newspaper back in school and we did this article about a historic clock tower on campus, Tomlin Hall. I made the headline for the article: Tomlin Is Timeless. Note that the clock tower wasn't broken or anything. Fast forward to the present. My coworker is now arguing with me whether or not this is an example of a pun or a case of irony. She feels it's a case of irony. It is my contention that is in fact an ironic pun. Now, I did not arrive at this decision lightly. She says you can't have your cake and eat it to, but I do not see why you couldn't have an ironic pun if it does in fact fit the definition of both. So now I put it to you: Is "Tomlin Is Timeless" a case of irony, a pun, or truly in fact an ironic pun? Thanks.