Is it possible to transfer edited photos on Lr6 from one imac to another with Lightroom classic?

You are not going to lose those images because they are not "in" Lightroom. They are in folders on your computer. I think the best thing you could do is purchase your new computer from a reputable dealer, and have them transfer all of your images, exactly as they are organized on your current computer, to the new one. Have them transfer all of your user files to the new computer, exactly as they are organized on your current computer. Then, it would seem to me that all that would be necessary would be to install Lightroom Classic. It would find the catalog you were using previously, and would upgrade it by creating a new copy of it that is compatible with Lightroom Classic. Then Lightroom Classic would open, and if the images are positioned as they were on the old computer everything should simply start normally and you can go to work in Lightroom Classic.

It might all seem like a big mysterious and scary step. But in reality it really isn't. I had to make the switch once to a new computer and it seemed like a daunting task. I followed the steps I outlined above, and it was seamless. It just worked. Nothing to be afraid of, in my opinion.

"I'm fearful about getting a new imac in that my very old (30 year-old and more), precious, already edited photos on Lr6 won't be able to get transferred to a new Lightroom Classic I will be installing on the new imac."

Well don't be afraid, this is a built in feature of Lightroom 6/Lightroom Classic.

Instructions: https://www.lightroomqueen.com/how-do-i-move-lightroom-to-a-new-computer/

Please read them carefully, and follow them exactly. Do not try steps that are not specifically mentioned. Pay particular attention to #6, which specifically instructs to NOT import photos.