Yes, you can.
You can download Lightroom on the other machine : Direct Download Links for Lightroom 3 and Photoshop Elements 8 | ProDesignTools
and license it using the same serial key which would be present under your Account : Adobe ID
If you want to access the same catalog, then you need to transfer your Lightroom Catalog along with the original images to the other machine.
Refer this tutorial for the same : How to Migrate LR to Another Computer | The Complete Picture with Julieanne Kost | Adobe TV
Wow! Thank you SO much. I like your answer better than the previous one which said NO …."CS6 and earlier programs have not been tested and will not be updated to run on Mac El Capitan
-which means that you try to use CS6 and earlier at YOUR risk of having problems
-you may get CS6 and earlier programs to install and run, or you may not (some do, some don’t)”
I will try your suggestion tomorrow….now then, can I still lay my hands on the series key of which you speak…that is the question.
Again, thank you very much.
Well, that answer was right if you are on Mac El Capitan.
I shared the normal procedure to transfer Lightroom 3 program to another machine unaware of the fact that you have El Capitan operating system on the machine.
It is correct that Lightroom 3 has not been tested on Mac El Capitan so, it might or might not work.
You can probably install it from the link that I shared and check that.
Again I thank you for taking the time to write again. I will take you advice and ‘try’…I should find out very quickly if the answer is emphatically ‘no’...