Biz or Eco?
Flying Blue shows availability for IAD-AMS-NBO-LUN. I have no idea what KE's policy is regarding these flights, but DL would definitely be blocking the IAD-AMS flight. Plus, the fuel surcharges will be around 500/ticket at least.
Ethiopian has Biz availability leaving on 30th, connecting on 31st to LUN. That's about as good as it gets. All bookable on United - the award booking engine for dummies
If you want economy, it probably will require a European connection, which will force you to leave on the 29th to make that nonstop flight to LUN (on 31st) since it leaves in the morning. There is no availability on the 1st to LUN from ADD, although you can connect in JNB
