You can, by hand, redirect the various files the native Lr application creates and reads at runtime once installed (and run once). About the only thing you can't, as far as I know, is the platform specific settings properties, which end up where ever the OS says a particular login preferences should go.
But the raw cache, photos, catalogues, plugins (though, again, these are assumed to be in your user "Documents" directory now, I recall), etc. can all be set to specific locations.
This is the nature of native apps; most users want the app to feel "native" and not like a port or a web app. Therefore, following the platform specific recommendations for app defaults and letting the user change where user data goes (with recommendations) has been the gold standard for years.
I know of no way to "sandbox" the native app to a single file system area as one can a web app.