Retrieve photos from lost smartphone

OK now I've found your duplicate thread and merged the two.

If you backed them up to Google, logging in to your account should be enough to run the software you used to back them up, to be able to retrieve them.
The proper answer to that question is "from your backup" but I'm guessing you don't have one. Your only hope might be with the local Police in case the phone was found and handed in.

When you take photos again, backup them up to the external SdCard and back both copies up to a computer via a USB cable.