This simple fix works for both Steam and GOG versions of Tomb Raider Legend. It fixes the game getting black screen and then crashing right after the game intro, it also fixes random crashes (but not for next generation content ON - this one you have to search for a patch elsewhere).

These are the steps to fix the game crashing:

1 - Go to Windows Defender app
2 - Go to Browser Control
3 - Go to Exploit and protection
4 - Scroll down and turn DEP off
5 - Save the settings, restart your computer and you're good to go