The marketing carrier is UA. It's UA ticket stock on a UA flight number. That is true even if another carrier operates the aircraft. Thus, the UA allowance will apply to all segments of the ticket, both outbound to DEL and on the way back to ORD.

OP's separate problem is the the baggage allowance on his e-ticket is established as of the date the ticket was issued. If his status has "increased" since that date, he should reprint his e-ticket receipt and see if the allowance has caught up with the change. If it has not, he should get that fixed now, not at the airport.

For *A, the agent will see a baggage allowance as specified on the e-ticket receipt. That will same time fighting at ORD (where it may eventually get fixed) and with LX at DEL (where it will be futile to argue).