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How do you unbind Alt? Can this be done in one of the games files? You can add your own bindings in the games menu but it still keeps Alt as jump. This is a problem because I can't Alt-Tab out of the game (the game takes the keys function away from Windows).

Not being able to Alt-Tab means I can't get out and back into the game and maintain fullscreen. When the game starts, after the intro and menu, it is black with no sound until I Ctrl-Alt-Del, then Esc to the desktop then click on the game in the taskbar to get back to the game, however it is now in a low res window with the taskbar. Of course Alt-Enter don't work either because Lara just jumps.

Also, not being able to use Alt means I can't click on any of the DOSbox tools.

GOG should really have sorted this out, the game takes fricking ages to set up and even then it isn't quite right.
You can also press the winkey (start) to go to back to the desktop, and also Ctrl-Esc.

You can also use this to remap dosbox's keyboard.

http://www.dosbox.com/wiki/Mapper

Personally, I think you should try with ctrl-esc or winkey as it should also do the job, but you can also remap dosbox's keyboard.
Both the winkey and ctrl esc are disabled in the game. Well, they are for me because nothing works other than ctrl alt del. Though I did manage to get ctrl F10 to bring the DOSBox tool menu to appear but the mouse cursor won't go up far enough to click on anything!
I have just tried alt-tabbing from Tomb Raider on dosbox. Using either winkey or ctrl-esc works fine here.

What are your system specifications?