How to convert .LQT audio files to .MP3 format

You can try to play .LQT files with LiquidPlayer and Real Player.

You may also use Liquid Audio/LQT plugins for Winamp. You may try to find Official Liquid Audio plug-in or, for example, you may try the following one
http://www.geocities.com/liquid_aac/

With a Winamp LQT plugin you should be able to convert to another format (say MP3) using Disk Writer output plugin. If you have any other player or converter that can use Winamp plugins (such as DBPowerAmp) you can try to use it to convert .LQT audio files to .MP3 or any other format.