You've been given great advice. I'm so sorry for the loss of Lulu. Sometimes there are underlying conditions that can cause sudden deaths.
iHeartPieds is correct and Kuku will need time to grieve. If eventually you would like to get him another friend, remember that the new budgie will need to be quarantined in a room away from him in a separate cage for 40 days to ensure that the new budgie does not spread an illness to Kuku.