I am definitely not sure, so I am totally guessing. I suspect that Delete_management isn't made to interact with python/arcpy objects directly, same as many arcpy functions. It's possible that esri is slowly adding support to act on these, but if it were supported, I don't see any reason for an in_memory feature class/set. I tried this and got okay results:
I am guessing that most arcpy functions act on file-like objects, so by creating in_memory file like objects, people could use those functions. I don't know anything about future plans or anything. this is all guessing. I would stick with in_memory feature classes for now.
line_shapefile = "C:\Users\jhook\Desktop\lines.shp"
output = "in_memory/output"
for i in range(0, 100, 1):
geom_obj = arcpy.CopyFeatures_management(line_shapefile, output)