Lightroom is not supported on Chrome OS which you are using in your Chromebook.
Click to refer the minimum system requirements for Lightroom
Hope this helps.
Chromebooks are a new breed of computer, unlike regular notebook computers which run Windows or Mac OS X operating systems.
Chromebooks run the Chrome operating system and are specifically designed to be Cloud based and very Google-centric.
Because of this, they cannot run the usual software (Adobe, Microsoft) that Windows and Mac computers run. You must run Chrome software (known as apps) specifically written for Chromebooks.