Where does the chart require you to be at 5000' over LZR?
It's not on the VOR chart, but part of the TERTO 1Q STAR.
With an MSA of 3500', once cleared for the approach and within 25 sm, you may descend to the MSA.
Why does a clearance for the approach permit you to descend to the MSA? (i.e. what's the regulatory/ICAO reference for that?)