From LightWiki

The Program disc for LightWave 3D [8] works on both Windows PCs and OSX Macs, so you can install on whichever platform you need and then you need to just re-register.

For LightWave 8.x or below: If you bought your LightWave through NewTek US, you need to use http://register.newtek.com, if you got it from NewTek Europe, then it is http://www.newtek-europe.com/register.htm.

For LightWave v9: Update your account at http://register.newtek.com

The reason for reregistration is that your dongle may report a different number on the Mac to the PC, or your license.key will be different, and thus your permanent license.key will not work across platforms. However, you can put both numbers into one license.key file so that you can simply carry the dongle, license.key and program disc wherever you go and install LightWave on whichever Windows PCs or OSX Macs you come across and use your full licence there.

If you are using LightWave v9 and need to know how to get a license.key for your new platform have a look here.