Charges for Changes and Cancellation are waived - even on the absolute cheapest fares on EK - but unfortunately there may be a fare difference to pay if your sister-in-law is (presumably) moving her return travel date to sometime immediately, as flights to London at the moment are looking very, very full.

Your sister-in-law will need to go to the EK office in Lusaka (it's in the center of town) with a copy of the death certificate who can then make the arrangements.