Oh, sorry, I assumed too much.
If you're running Mathematica, you can just open a new notebook (File -> New -> Notebook). Copy the Lissajous3D code above, and paste it into the notebook. What you should have at that point is an Input cell. You'll see a bracket at the right side. With the cursor anywhere in that cell, tap Shift+Return. It won't produce any output, but it will have evaluated that code so that Lissajous3D is available to use like any other function. The cursor should now be below that cell. You can also just click anywhere in the whitespace below the cell to make sure. Now copy the whole ParametricPlot3D expression. Paste it into your Mathematica notebook. Again, with the cursor anywhere in this new cell, tap Shift+Return. This time it should output the plot, and it should look like the picture I pasted above. You can now tweak things in the ParametricPlot3D cell (don't need a new cell), and Shift+Return again.You can also tweak the Lissajous3D definition and Shift+Return that cell, and the next time you Shift+Return the ParametricPlot3D cell, it will use the updated definition.