I lost my phone, can I recover the data from my Google account? I've lost my smartphone (Samsung Galaxy Star duos) last month. And now I realized that it contained very important data of mine. I believe that my phone was connected to the Google account almost all the time.

My question is, "Can I get my data (photos) back, from my Google account (connected to my phone)".
You're probably SOL since the battery is dead by now. Still, on the off-chance it isn't, check out Plan B (described at http://www.digitaltrends.com/mobile/how-to-track-a-cell-phone/). When you install an app through the Play Store on the computer, it is automatically installed on your phone. 

If you used some service that syncs photos or other data somewhere else (e.g. syncing photos to Picasa) then you could find everything you backed up there. If you didn't, then you assumed this risk by placing all your eggs in one basket and never transferring data off of your phone. Perhaps your service provider had some automatic backup software running (e.g. Verizon backup) in which case you could contact them to ask how to recover data.

The fact is, if your data was that important, you should have taken steps to protect it ahead of time, and you should not have waited so long to try and locate the device; and now you are faced with the consequences of that negligence. 

If you choose to keep all of your critical data on, say, a thumb drive, or an external hard drive, or a CD/DVD-ROM, and you have no backups and you lose that device, then, whoops, that's the risk you assumed by keeping it all in one place. It's the same with your smartphone.

Steps to protect it include anything that generally backs up your data elsewhere (be it specialized software that syncs photos, or general software e.g. MyBackup Pro), and any software that may help you locate the phone if it is lost (see the link above for more tips there).