To fix the steam_api.dll missing Tomb Raider (2013) , you should first attempt to verify your game files through Steam rather than downloading the file from third-party sites
If it still crashes, run the game in Windows 8 Compatibility Mode: tomb raider 2013 steamapidll download new
Steam will automatically detect the missing steam_api.dll and download a fresh, safe copy. Troubleshooting Common Errors To fix the steam_api
When you play Tomb Raider (2013), the game uses this file to: Ignore third-party DLL websites
Method 2: Download Steam API DLL manually
steamapi.dll is a legitimate Steam client file — it’s part of Steam’s DRM and online features. Downloading it from unofficial third-party “DLL download” sites risks malware, ransomware, or spyware.