For the mileage accumulation on Air Canada code-share flights operated by another Star Alliance airline, refer to the "Earn Miles" section of the airline operating the flight.

and at LH section:

Eligible flights
All scheduled flights operated by Lufthansa, CityLine and LH Train service: Frankfurt - Cologne and Frankfurt - Stuttgart are eligible*†.

Please refer to the tables below to see how many miles you'll earn on flights.

Mileage Earned‡§

All regular scheduled flights except for Intra-European flights**

Booking Class Aeroplan Miles

(F, A, C, J, D, Z, Y, B, M, H, Q, V, G) 100% of miles flown (minimum 500)
(W, S, U) 50% of miles flown (minimum 500)


Intra-European Flights**

Booking Class Aeroplan Miles
(F, A, C, J, D, Z) 100% of miles flown (minimum 500)
(Y, B, M, H, Q, V, W, S, G, U) 50% of miles flown (minimum 500)

Class of Service Bonus:
First Class: 50%
Business Class: 25%

It appears that K gets nothing.