Currently, the route settings is a bit limited in ATK. You can only either do route+points_per_segment, or k_points.
For your purpose, I would stick to the route+points though. If you want GXUZG route, just use
bandstructure = Bandstructure(
configuration=configuration,
route=['G','X','U','Z','G'],
points_per_segment=20,
bands_above_fermi_level=All,
projection_list=ProjectionList(elements=[Lanthanum,Manganese,Strontium,Oxygen]),
)
If you want the route you indicated, just use
route=['G','Y','Z','G']
because that's what these k-points are called.