Yes, you can install Lightroom on two computers. However, you can only be signed in to Creative Cloud on two computers at a time. If you want to use Lightroom on a third computer, you will need to sign out of Creative Cloud on one of the other two computers.

You can also use Lightroom Classic and Lightroom on the same computer. However, you will need to have a separate Creative Cloud plan for each application.

If you are using Lightroom Classic, you can use the same catalog on both computers. However, you will need to make sure that the catalog is stored in a location that is accessible to both computers.

If you are using Lightroom, your photos will be automatically synced between all of your devices. This means that you can start editing a photo on one computer and then finish editing it on another computer.