The line that includes your query is escaping quotes wrong-- this doesn't work:
" " \Layer\ " LIKE 'BOUND%' AND " \Layer\ " NOT LIKE 'BOUND-ADMIN-VIR' "
The quote escape works like this: \" ...or this: \'
So try this: " \"Layer\" LIKE 'BOUND%' AND \"Layer\" NOT LIKE 'BOUND-ADMIN-VIR%' "
Test it - and if your single quotes are also giving trouble (I don't think they will), then try this: " \"Layer\" LIKE \'BOUND%\' AND \"Layer\" NOT LIKE \'BOUND-ADMIN-VIR%\' "
You can eliminate the confusing escape characters by using string substitution and the AddFieldDelimiters function.
query = "{0} LIKE 'BOUND%' AND {0} NOT LIKE 'BOUND-ADMIN-VIR'".format(arcpy.AddFieldDelimiters(Polyline, 'Layer'))
arcpy.FeatureClassToFeatureClass_conversion(Polyline, Fea_Class_Path, "PCL_LN", query)
Also, I don't see your Polyline variable declared anywhere.