The £1,250,000 - from a £3m fund for cultural development - was voted through by a committee, and has now been agreed by the full council.
The old building is due to close early next month for the £17m redevelopment, but before construction begins 95% of the cost had to be raised.
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The new Lyric is to be built on the site of the current theatre on the banks of the River Lagan in the Stranmillis area of Belfast.
In November, the theatre was given £250,000 by the Foundation for Sport and the Arts and in June, a private donor pledged £1m on top of the funding already promised by government departments.
Ballymena-born international star, Liam Neeson is among the several thespians to have had started their careers in the early days of the theatre, and has now joined the various artists supporting the renewal plan.
(BMcC)
