joejpe123,
I am guessing that your lacie is a real hard drive, not a thumb drive.
If so you can run programs from it just like any other logical drive on your computer.
The caveat is that is must be installed to that drive, not just moved over as a file.
In addition, lets say you install photoshop on lacie and it is drive G: for example.
It will work on your computer that you installed it form but if you unplug it and move to a separate computer and try to run it, it will not work as there are registry entries that are on the main source drive... ie. usually C:
You cannot run it from computer to computer unless you reinstall on each so that all of the filters, registry entries, scratch disks etc. are in place.
We won't even discuss the licensing issues this causes you from Adobe.
If it is a thumb drive then that is another matter. Some open source software is available for thumb drives and some drives such as the U3 variety can run some software.
So far though, there is no legal way to run Photoshop from a thumb drive.
Tim