Found a workaround:
1) You need to have TRLA installed on your PC (obviously) and TR3 too.
2) Download the TR Multi Patch updater from here: http://www.tombraiderchronicles.com/vista/patch.html
and install the updates. IMPORTANT: you must install the TR3 update especially: this is not going to work without it.
3) You've done that? Good, this is where it gets interesting. In the folder where TR3 is installed (usually C:\....core design\Tomb Raider III) right click on on the tomb3.exe file and select "copy"
5) Go to where TRLA is installed (usually C:\.... core design\Tomb Raider - The Lost Artifact) and paste the tomb3.exe file here.
6) Rename this file tr3gold.exe
7 Copy the following folders from the TRLA CD-ROM:- DATA, FMV, AUDIO and PIX to the TRLA folder on your HDD.
8) Go into the DATA folder: theres a file in there called trtla.dat - rename this TombPC.dat
Thats it. You can now play TRLA without any CD's in the drive.
Thanks a bunch, Malleus! Worked flawlessly.