I purchased LR some years ago & want to download it again on my new computer

If you registered with Adobe (or purchased from Adobe) then they will have your serial number at account.adobe.com, sign in with the e-mail you used when you made the purchase, then click on View Billing History, then click on Products, you will see your serial numbers. Again, this assumes the IF at the start of that sentence is correct. When I do this, I see my Lr 2 serial number (and Lr 3 and Lr 4 and Lr 5 and Lr 6 serial numbers).

If you don’t see your serial number there, then the only other way to retrieve your serial number is if the computer that you used to run Lr is still available.

I agree with ​@Jim Wilde that there is little chance that you will find a download file for Lr 1 or Lr 2, and virtually zero chance that it will run on Tahoe.

ADVICE: from now on, no exceptions, you need to mark down all of your serial numbers (not just Lr) in a text file that is shared to the cloud, so you can always find your serial numbers if you need them.