Fahad Musanan, who is a professional footballer in the Ugandan Premier League, was watching the game on television with friends when he fainted after Lampard made the scoreline 1-1 against his former club.
According to Kawowo, the 24-year-old was rushed to Bombo Military Hospital, but was pronounced dead upon his arrival.
The Federation of Uganda Football Associations released a statement on its website saying: "FUFA is in shock after receiving news about the sudden death of Simba FC player Musana Fahad in Bombo this evening.
"The body is currently at the Bombo Barracks Hospital. Burial arrangements will be communicated later."
Lampard joined City on a six-month loan deal after signing for MLS side New York City on a free transfer at the end of last season.