I had no idea that the first three Tomb Raider games were available on Steam but, yep, they're all there. However, they're the original DOS ports running through an emulator, which throws up a bunch of performance, resolution and control problems. Thankfully, more modern remasters are on the way that will run at 1080p with 60fps.
Realtech VR is the company handling the remasters, and it's basing them on the mobile versions of the games. You'll need to own the games on Steam in order to play the remasters because they're essentially mods of those versions, but if you do then they'll be completely free. The developer says it's looking at doing the same for GOG but isn't sure if it's going to be possible.
Along with a new 3D engine, the remasters will offer support for OpenVR, feature a range of graphics options and be playable with a controller. Realtech VR hasn't yet set a release date.
TR1-3 remaster for PC are planned for Steam for free and will requires the purchase of the DOS version being sold on Steam (like ZDoom playing Doom games). Also the PC version will supports OpenVR and features a new 3D engine for both 3 games.March 1, 2018
Realtech VR was founded in 2008 and has largely worked on games for iOS, although its website says that its team has experience in PC development. It has already finished the first two games and is currently working on Tomb Raider 3. Since the announcement, fan questions have been pouring in, and Realtech VR has been dealing with them on Twitter—click here to read its responses.
You can watch videos of its work on the first two running below, and everything seems to be as promised. A trailer for the remaster of Tomb Raider 3 is coming next month.