[1] Ofungi was born in Padolo Village, Okoro County, Nebbi District, West Nile sub-region, Northern Region of Uganda.
On 1 August 1974, Inspector General Luke Ofungi was sent on leave by President Idi Amin after defying the dictator openly at a security meeting.
On 15 May 1980, he was appointed Inspector General of Police, serving in that capacity until 1 May 1981, when he took leave of absence, under the government of President Milton Obote.
On 1 November 1985, following the overthrow of the Obote II regime, Luke Ofungi was re-appointed Inspector General of Police by Tito Okello.
The Uganda government cleared him of what were proven to be false charges and went on to posthumously appoint him on contract effective November 1, 1989, for 24 months.
During his leave he focused on the tour and travel company he had set up in the 1970s and with his wife Claudia Kinobe, and continued to run a confectionery and restaurant called Confe in Kampala.