I want to change this information, with python:

I have this code (got here: https://community.esri.com/thread/43148 ) , but it changes the layer name. I want to change layer label.
It is a simple feature, with no unique values.
import arcpy, os
from arcpy import env
env.workspace = os.curdir
for mxdFile in arcpy.ListFiles("*.mxd"):
mxdPath = env.workspace + "\\" + mxdFile
mxd = arcpy.mapping.MapDocument(mxdPath)
layers = arcpy.mapping.ListLayers(mxd)
for lyr in layers:
if lyr.name == "old name":
lyr.name = "newname"
arcpy.RefreshTOC()
mxd.save()<SPAN class="line-numbers-rows"><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN><SPAN></SPAN></SPAN>