What version of Lightroom Are you using? If it is the cloud version, you cannot have the app nor the library anywhere else than on your internal hard disk. The version called classic has to have the app itself on the internal hard disk but its files, both the catalog and the images, can be anywhere.
I am assuming that you are using the cloud version (called Lightroom Desktop very counterintuitively) and that version automatically manages the disk space it uses by dynamically downloading and offloading the images it needs. If you choose to store local copies of images, there is a setting in Lightroom Desktop that allows you to put the local copy of images in any location you choose. The cloud version stores all images in the cloud and the local copies are just used as local working copies. It is typically best to just use the default settings and just let Lightroom manage local storage and not store your entire library on your own hard disk(s).