LAME is not a stand alone product but rather some code that can be wrapped into another program to provide MP3 encoding capability. There are some simple GUIs written to interact with LAME. But, since Audacity is free, I would just download and use it. You get the MP3 capability and a whole lot more - like recording, editing, effects, noise reduction and saving in numerous file formats (other than MP3).
Go for it.
Excellent replies, all! I already have some Windows software that will generate a wave file. Does that mean that all I need is LAME? Or should I also get Audacity too? (Audacity has some interesting features that are very useful, such as noise reduction.)