Export LRC collection to a file

Depends what you mean by "export a LRC collection to a file".

If you want a text "List" then a plugin like 'List View' is useful-

http://www.beardsworth.co.uk/lightroom/list-view/

Or a way to simply obtain a 'list' of filenames- A Script to 'Get Filenames'-

http://lightroomsolutions.com/a-quick-list-of-filenames/

If you want to export Photos to a folder (file?), then it is the Export dialog you want. Export any selected photos whether they be selected in a Folder or Collection.