The employee was a teacher working at the Lyric Theatre run by the authority in May 2007.
The Health and Safety Executive told Llanelli Magistrates Court the council had not taken all practicable steps to ensure the safety of employees and others.
The council, which pleaded guilty, was fined £20,000 each for two health and safety offences and £5,000 for the lift equipment offence. It was also ordered to pay £7,712 in costs.
Speaking for the council Dafydd Enoch QC said: "The prosecution has been based in essence entirely upon the very full report commissioned by the council. This is a council with an excellent record. This is very much out of character."
A spokesman from Carmarthenshire County Council said the council takes health and safety "very seriously".
He added: "We would like to assure the public of the safety of the Lyric Theatre and other buildings owned and managed by the council."
Welsh council fined 45,000 for health and safety offences
Carmarthenshire County Council has been fined for health and safety offences after an employee fell down a lift shaft.
