Paid for LR classic in 2015 & now trying to move it on 2019 iMac. Won’t let me.help!

As it sounds like you will be subscribing to an Adobe Plan, be aware of the difference between what Adobe now calls two different applications, Lightroom (Lr) and Lightroom Classic (LrC)

see:

Lightroom Classic vs. Lightroom CC: Adobe

Lightroom Classic is the newer better Lr6 in effect. Lightroom is not.

Lightroom (Lr) is also known at Adobe as Lightroom Ecosystem (Cloud Based), as Lightroom Desktop (odd that one) and has customer based nickname Lr Cloudy. Blame Adobe marketing for any confusion. It uses an album on the cloud and stores photos on the cloud. It has less capability than Lightroom Classic. Basicaly this is a product for the smart phone customer base.

Lightroom Classic (LrC) is what you are used to. It uses a catalog on a hard drive, and normally you save photos on a hard drive. 

When you look at the Adobe Plans, be aware that while Lightroom is available as a one app plan (the Lightroom Plan), Lightroom Classic is not, this has fouled up more than a few irate customers. The normal plan to get Lightroom Classic is the Photography Plan (includes Photoshop, Lightroom, Lightroom Classic, PS on iPAD, Lightroom Mobile, Portfolio, ans some cloud storage)

The new, modern Lightroom Classic IS a desktop version. You only need to be connected to the Internet to download it and install the regular updates. You will be amazed at all the features and enhancements that have been added, making LR6 look like a clumsy dinosaur. And, as far as Adobe is concerned LR6 is a dinosaur which is no longer supported. Here's the status page from their website:

https://helpx.adobe.com/lightroom-classic/help/lightroom-6-end-of-support.html

As indicated, you didn't have Lightroom Classic. You had an older standalone version of Lightroom. Subscribing to Lightroom Classic doesn't mean that you have an "all to the cloud" version of Lightroom. Lightroom Classic still installs locally on your computer FROM the cloud and is updated FROM the cloud on approximately a quarterly basis. But everything functions locally just like your ancient, out of date, obsolete version of Lightroom functions. It is no longer offered by Adobe and is no longer supported by Adobe. And it cannot be installed on the new operating systems because the installer is 16-bit.

There was no Lightroom Classic in 2015, you cannot claim to be a Lightroom Classic user or have a Lightroom Classic license; so what did you purchase?

Was it Lightroom 6?

Lightroom 6 cannot be installed on Monterey; however I have read that you can install earlier operating systems on an external disk and then use that earlier operating system to install Lightroom 6.