This issue should only occur on some older Intel integrated graphics devices.
To get around it, open the Intel graphics properties window by pressing Ctrl + Alt + F12 (here are other ways to access it - click here for details).
Look for the 3D Settings (might be named OpenGL settings - click here for details) and set the "Depth buffer Bit Depth" to "24 Bit Depth Buffer".
Confirm by pressing OK in both windows, then launch the game.
It would be advisable to switch this setting back to Default once you no longer need the custom setting to play Tomb Raider 1.
Alternatively, you can try using nGlide instead of the default OpenGlide solution. To do this, you should rename the glide2x.dll file, found in the \Tomb Raider 1+2+3\DOSBOX\ folder, and install nGlide (http://www.zeus-software.com/downloads/nglide).