Will I have to pay for luggage if WS operates on one segment of the fare?
 

I just booked airfare to MSY. I do have to change flights at LAX where DL will fly me to MSY. Since DL operates that flight, will I and my companion have to pay for luggage if I have the WestJet RBC World Elite Mastercard?

Only on the return trip.

You aren't going to re-check your bags at LAX, you will check them with your WestJet baggage allowance. When you check your bags on the return trip Delta's baggage rules will apply.

Does WJ not have reciprocity benefit agreement such as free luggage for elite members with Delta? I spoke with a WJ checkin agent and was told that Delta elite members get free check bags flying WJ. Not vice versa?

Oh, that sounds like an improvement over last year. I have had the Westjet bag fee waived a couple of times, but also a couple of times that it was not. It seemed all to depend on the agent and/or airport. Good that there now seems to be a rule.

Reciprocity for a credit card perk seems unlikely.