I lost my iPhone and never did a back up. Is there anyway to recover my pictures?

I lost my iPhone and never did a back up. Is there anyway to recover my pictures? - 1

Did you import them on the iMac?

Unless you had Photo Stream and or iCloud Photo Library enabled, no

Either you had a backup or you didn't. There's no magic button other then that.

No there isn't any way left now, and in case you need a good security app you can have Leo Privacy Guard, it will solve all your problems.