Now I know that saving layer files as lyr format is "not in production" despite many of us scream for this functionality, but I have come across a chicken and egg situation. About 9.9 times out of 10 when someone sends me a shapefile with the associated lyr file they have not created it with a relative path so the lyr file is pointing to their local machine.
In ArcMap you can right click on a lyr file in the catalog panel (or ArcCatalog) go to properties and reset the data source path and this updates the lyr file. You are then able to add the layerfile to the map and display the data.
Would be very helpful if ArcPro can expose the properties of a lyr file so these sort of errors can be fixed.
I could do it in ArcMap, but I'm using pro and bringing in the broken lyr file into ArcPro, fixing the data source internally is no use as I can't save it back as a lyr file! No point creating a lyrx if everyone else is using ArcMap...