I'm pretty sure that the first ever Tomb Raider appeared on the Sega Saturn. But it was widely successful on the playstation. Where the majority of future games spawned.
May I bring to attention the name of the thread, it says Sony. Therefore it need not be only focused on PSX. True all of the Tomb raiders have been on the PC, but they also have all been on the Playstation (PS1,PS2 and PS3). Icons tend to carry themselves throughout a console's evolution. It's massive popularity on the Playstation is sufficient enough to call it a Sony Icon.