Throw the box away; it's not helpful here. What you see when you look through the time lens is a live cat, then either a) nothing happens or b) it suddenly turns into a dead cat. What you don't see is the cat's death, if it occurs. Look at the graph in the article; light moves from left to right through one spatial dimension, and from bottom to top along the temporal dimension. You see the before and after, but not the in-between moment.
Instead of a cat, consider a situation where you could 'use' this time lens, if it operated over human-scale time periods. I sneak the time lens into your party, disguising it as a beer keg. At an appropriate moment, I trigger it; then I rush over to your wall safe, open it and extract the diamonds stored within, close the safe, and return to my starting position. From your point of view, everything is as it was before. Unless you were looking at the clock - in which case you would see it jump forward by two minutes! You realize someone at the party has been using a time lens, and raise the alarm. Suspicion soon falls upon me, and I shamefacedly produce the diamonds from my pocket.
But just as you and your friends are about to lay hands on me, I vanish! I triggered the time lens again, and slipped out between you, unobserved.
Of course, I can't see what's going on with the time lens either, in all likelihood; perhaps I need some sort of ninja skills to move blindly through the temporal hiatus.
Above the mantelpiece, where else? Seriously, I just threw that in because most people have a clock (or several) and ISTM that you would experience a forward jump in time if this hypothetical device could work as described. Not having read the paper yet, I don't know if it would only work for people observing things from a particular perspective, or whether it would just create a bubble of 'extra' time for anything within its field, during which observations from outside would be impossible. Of course, this might make it impossible to escape as well - I took some dramatic liberties with my scenario to explore the possibilities, although I left out some of the wilder ones that came to mind.
Instead of a cat, consider a situation where you could 'use' this time lens, if it operated over human-scale time periods. I sneak the time lens into your party, disguising it as a beer keg. At an appropriate moment, I trigger it; then I rush over to your wall safe, open it and extract the diamonds stored within, close the safe, and return to my starting position. From your point of view, everything is as it was before. Unless you were looking at the clock - in which case you would see it jump forward by two minutes! You realize someone at the party has been using a time lens, and raise the alarm. Suspicion soon falls upon me, and I shamefacedly produce the diamonds from my pocket.
But just as you and your friends are about to lay hands on me, I vanish! I triggered the time lens again, and slipped out between you, unobserved.
Of course, I can't see what's going on with the time lens either, in all likelihood; perhaps I need some sort of ninja skills to move blindly through the temporal hiatus.