After going through the activation process, your LPCXpresso IDE (v6 and later) license files are stored in a directory called "NXPLPCXpresso". This is the same regardless of whether you are using a Free license or a Pro license.
The location of this directory depends on the host operating system, and the directory must be writable by the user running LPCXpresso IDE.
The location of the directory is %ALLUSERSPROFILE%, where %ALLUSERSPROFILE% is an environment variable whose value is typically "C:\Documents and Settings\All Users".
The location of the directory is %PUBLIC%, where %PUBLIC% is an environment variable whose value is typically "C:\Users\Public".
The location of the directory is "/usr/share".
The location of the directory is "/Users/Shared".
Earlier Code Red toolchains stored the license directory in the same root directory as specified above. However the name of the license directory itself was different. This allows different toolchains to be installed and licensed at the same time.