The club was founded in
Lysi,
Famagusta on June 26, 1932. Club founders were Ch. Fokaides, Ch. Panayides, K. Rousi and N. Petrou. The choice for the club's name is attributed to Demetris Lambrou. The club had its own stadium in Lysi. The stadium was called «Grigoris Afxentiou Stadium» as a memory of EOKA hero Grigoris Afxentiou who was born in Lysi and he was a player of ASIL. ASIL stadium was one of the first stadiums in Cyprus with grass. After the 1974 Turkish invasion, ASIL used
Tsirion Stadium in
Limassol as its ground and since 1978 the club is based in
Larnaca. Since 1984 ASIL has a new stadium in Larnaca called «Grigoris Afxentiou Stadium». In 2019–20 season ASIL used
AEK Arena as its ground and since 2020–21 season ASIL uses
GSZ Stadium. The best season for the club was 1968–69 in which they finished 6th in the
first division. ==Colours and badge==