Lightroom 3

the license you will be buying is illegal.  it's a certainty the vendor (who may have a valid license) does not have authorization (from adobe) to resell the license.

ie, that license can be revoked (by adobe).

Beware of fake Adobe reps who may contact you privately offering to sell you software or take control of your computer. It's a scam, run away! Real Adobe employees will never reach out via Outlook, Yahoo, Gmail or Skype.
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3 Easy Ways to Identify Genuine Adobe Staff
https://tinyurl.com/10791730

When you buy & install discontinued software from untrusted sources like auction sites, you're getting a pig-in-a poke. 

• DO NOT give anyone your payment card or other personal information. 
• DO NOT expect the disks to work. 
• DO NOT expect the license to be legitimate. 
• And DO NOT complain later when your computer is infected with malware or you become the victim of a RANSOMEWARE attack. 

You can avoid all of these pitfalls by purchasing legitimate software directly from Adobe.

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Lightroom on desktop, mobile and the web
• Lightroom Classic
• Portfolio website + hosting
• Creative Cloud Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).

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

Creative Cloud Plans
https://www.adobe.com/creativecloud/plans.html

Hi, can anybody please tell me if I can still install and use Lightroom 3 as I have noticed that I can buy a copy on ebay. 

By @neilp75431277

Be aware of buying a illegal copy or a cracked version. The versions offered on Ebay are often illegal.

Adobe doesn't support it, they only support the current product.

But can it be installed? Yes, unless it is from the bundles CS/CS2/CS3/CS4 which (Adobe say) have stopped licensing forever. So, ... Hmm.  Lightroom 3 was released in 2009.  That puts it in the CS4 years, so there is every chance licensing won't work. Beware too that much software sold on eBay is counterfeit and has viruses and worse.

Also, there is the question of system compatibility. It sure won't run on Mac OS Catalina or later. Any other current Mac or Windows system was long out of support.

You can get Lightroom and Photoshop in a bundle for $10 a month, subscription (annual commitment, auto renews).