It doesn't seem like the ENW to ENLX conversion is possible. However, when users create compressed *.enlx libraries in Endnote, it is likely that it also contains ENW files.
Convert EndNote citation file to EndNote archived library file.
We found one software available in the database for this conversion.
Apple iOS (iPhone, iPad, iPod Touch devices) software - convert enw to enlx on iOS
App for iPad used to search in bibliographic databases
Convert from enw file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.