So what does life time mean to you?
I assume a lifetime warranty covers manufacturing defects for the reasonable service life of the product. So a product that wears out or was damaged in use would not be covered. I would also expect that the warranty coverage had a reasonable time limit regardless of use. So if you bought a rack and stored it in its box for 15 years and then used it only to discover it was defective I would not be mad that the company didn't cover it under the lifetime warranty as the reasonable lifetime of that product from time of purchase had expired.
Coming at it the other way a warranty is like any other human transaction....in that it depends highly on the way the people involved behave. I know the internet lawyers will say they'll go to court to enforce a warranty on a $20 item, but they won't. Even on a bicycle it's unlikely that a warranty dispute is going to be settled anywhere, but between the consumer and some of the employees of the company.
You can get duds on both ends of that interaction. Consumers who are unreasonable/rude/etc... and employees who are rude/uninterested/etc... As the consumer you can only control your end of the interaction, but you can [in a lot of cases] try communicating with someone else at the company if you feel you are not getting a reasonable outcome.
I have been successful at getting warranty coverage for products that were clearly out of warranty. So it's not black and white. It's all about how you communicate and manage the process.
On a related note we bought a Yakima tray rack for the back of my GF's car ~8 years ago. Last year the part that locks it folded up or down in bike carrying mode failed. We contacted Yakima and they sold us a replacement at retail. Then one of the tray arms broke and we contacted Yakima and they sent us a brand new tray for free. If you read their lifetime warranty you could argue that either neither problem was covered or that only the failed fold lock was covered. What actually happened was totally different because life.
Given the cost of the rack [we bought it on 50% sale] and how much hard use it has had neither of us was going to kill ourselves arguing about the warranty coverage. We were polite, appreciative of the help we got and rolled with the situation. We paid a few bucks the first time and the second time got a freebie. Most importantly we got the rack working so we didn't have to put it in a landfill and buy a new one.
If I was the OP I would call again and hopefully speak to someone else who might be more helpful. It may or may not work, but it's worth another 5mins of your life.