Can you still purchase Lightroom or is it rental only?

I rent only and pay monthly.  Doesn't that include upgrads"

Lightroom is subscription based only. It comes in two flavors, Lightroom Classic continues the familiar local catalog with images stored locally on your computer; Lightroom stores images in the cloud and immediately makes images available to view and edit on all your mobile devices. The programs are designed for users with different needs and are excellent in meeting the needs of those users. The only Adobe product that I'm aware of that is NOT subscription-based is Photoshop Elements. It can still be purchased, and has a limited version of Camera Raw included with it. Additionally for video, Adobe offers Premiere Elements. Other than that, all other Adobe products are available by subscription only. The big advantage to the subscription model is that the programs are updated frequently, and the updates are all included in your subscription. You always have access to the latest version with all the most current features. It really is a good choice, in my opinion.

In the past, prior to the subscription model, you could purchase a license for Lightroom. You never owned the software; read the old (and new) EULA. 

Subscription only

https://www.adobe.com/creativecloud/plans.html

Warning, lousy Adobe Marketing and names given to  products

You will see two products related to what you consider to be Lightroom

Lightroom

Lightroom Classic

What Adobe now calls Lightroom, is a application that runs on your computer, saves Albums on the cloud, and saves photos on the cloud. It is not as capable as to what you would be using, pre subscription

Lightroom Classic, is run on your computer, stores catalog on computer, stores photos typically on computer. This is the app with origins back to Lightroom 1, 2, 3, 4, 5, and 6.

The app, you probably do not want, Lightroom, is also known as Lightroom Desktop (Adobe nickname), and by users, Lightroom Cloudy (derogatory), 

In the Adobe Plans, their is not a Plan for just Lightroom Classic. A plan for just Lightroom (cloudy) exist, you probably do not want that.

Most likely you want the Photography Plan, comes with Photoshop,  Lightroom  Classic,,  Lightroom,, Bridge,,  ACR..