Your save data is NOT lost, but the client is looking in the wrong place for it.
Your save file is located here: c:\program files\steam\userdata\<your user id>\35130\remote\autosave.lcgolsave
It needs to be located here: c:\program files\steam\userdata\<your user id>\35150\remote\autosave.lcgolsave
That is, the data is located in the folder "35130" but should be in the folder "35150" under "c:\program files\steam\userdata\".
Simply copying the file over likely not work as Steam Cloud now has the wrong file and will download a new file.
1. Make a backup copy of both folders..
2. From the Steam menu, choose "Go Offline" to put Steam in offline mode.
3. After Steam restarts in offline mode, choose "Exit" from the same "Steam" menu to shut down Steam completely.
4. Copy the save file from the 35130 folder into the 35150 folder.
5. Run Steam again. If it asks you to "Go Online" or "Start in Offline Mode", choose "Start in Offline Mode". This is critical, you must stay in Offline Mode for this to work.
6. Launch Lara Croft. Verify that you see your progress, and save your game.
7. Close Lara Croft.
8. Go to your Steam window and select "Go Online" from the "Steam" menu item at the top-left.
9. Run Lara Croft, verify that everything is still fine.
Please report back as to whether or not this solves the issue for you.