In the places I've worked it depends on how you get onto the LLZ.
If there is a fix positioned on final approach that an A/C can navigate to I just use "Cleared ILS approach RWY 23", I don't need a call established LLZ as I dont really care about the horizonatal positioning of the A/C, as the fix is already within the LLZ capture area.
If I am radar vectoring an A/C onto final approach then I am responsible for terrain clearance (normally radar terrain map) until the A/C resumes their own navigation.
Once I give a closing heading to intercept the LLZ I ask for a report "established LLZ". This indicates to me that naviagation (and therefore terrain) for the A/C has now passed back to the pilot ("Turn left heading 200, intercept the localizer, report established"). Once the pilot reports LLZ established and therefore back on their own navigation I use "Cleared ILS RWY23" for the vertical component of the approach.
I suspect you will get 500 answers from different parts of the world but this is the norm where I have worked, now and previously.