The last update to Lightroom 3 was issued in Dec 2011, so about 3 years prior to the release of OS X 10.10. Maybe another user who has tried would offer their experience.
I was so excited to get a new computer and camera... frustrating part is getting all the software (lightroom3 and photoshop cs4 ) to work together again :-(
If you have the License Key for your Lightroom 3 you can download the latest version from the link below and activate with the key and see how it operates.
Photoshop CS4 is a different issue and the License Key is specific to the operating system Mac or Win. You will first have to deactivate from the old system before you can install on the new computer.
The other option would be to have a look at the Creative Cloud Photographers plan available for a monthly subscription Photoshop CC 2014 with Lightroom included with the package.