OKAY folks, I’m delighted to say that I appear to have found reasonably definitive guidance on the question….
Now you have to try to remember exactly what phrase ATC cleared you with… DESCEND or CLEARED …. see below
If ATC clears the operator using the phraseology: “(Call sign) is cleared for the LAD 1 Arrival to Runway 23 at the XY airport”, the operator is cleared only for the lateral path of the arrival and ATC will provide permission to descend to altitudes as they want.
If the operator is cleared using the phraseology: “(Call sign) descend via the LAD 1 Arrival to Runway 23 at the XY airport”, the operator is cleared for both the vertical and lateral path of the published arrival and is expected to meet all altitude and airspeed limitations on the procedure.
Are we all done? 😁