When I create a layer using ArcToolbox, the input Featureclass gets removed from the available layers drop down list. In other words, if I want to "Apply Symbology From Layer" from the orignal layer to the newly created layer, ArcMap won't let me select the original layer as in "input layer". I have to restart ArcMap for it to appear again. Neither F5 nor saving the mxd changed anything.
I tried both 10.8.1 & 10.6.1 (on 2 different systems). I also tried a python script which fails (can't find the feature layer) on the second MakeFeatureLayer call:
mxd = arcpy.mapping.MapDocument("CURRENT")
df = arcpy.mapping.ListDataFrames(mxd)
inLayer = arcpy.mapping.ListLayers(mxd, "County", df)
field_info = arcpy.Describe(inLayer).fieldInfo
arcpy.MakeFeatureLayer_management(inLayer, 'outLayer', '', '', field_info)
arcpy.MakeFeatureLayer_management(inLayer, 'outLayer2', '', '', field_info)
Have you tried building this into a Model? I would try using Model Builder. Use Make Feature Layer again and the layer should appear as intermediate data in the model, then you can run subsequent tools on that intermediate data.