Walk in coolers are not lined with lead. They are made with steel, including stainless steel. Steel would prevent cell phone signals from entering or leaving the cooler if the door is closed. No need for a lead lining.
When Barnaby introduces himself and Troy to Derrick Seagrove, he identifies himself as "DSI Barnaby" - DSI is Detective Superintendent, while Barnaby is a DCI, Detective Chief Inspector.
Towards the end, Cully tells Barnaby that "Matthew" gave her lots of pictures of victim Isobel Hewitt for her photo exhibition, but the relation with all the photos (& who Barnaby told her to contact earlier) is named "Melrose".