Published Friday, 07 December 2012
Police believe the car park, driveway, parish hall and trees were targeted on Thursday night.
Local MP William McCrea said "every wall" of the Belfast Road building was painted.
"This is despicable and unacceptable," the DUP man said.
"Every wall of the building has been defaced.
"Glenavy Church of Ireland Church Hall has not only been attacked with sectarian graffiti but threats have also been painted on the walls about individuals."
Speaking at the scene, SDLP Lisburn councillor Pat Catney said: "This is the behaviour of morons.
"Cowards have descended under the cover of darkness and sprayed offensive, bitter slogans over trees and property. This is totally unacceptable and shameful."
The attack is one of a number in the area over recent weeks.
A War memorial and Orange Hall have also been targeted.
Sinn Féin MLA Mitchel McLaughlin said those responsible are trying to "drive a wedge" between the "good community relations" in the town.
He continued: "No place of worship should ever be targeted in this way. This is completely wrong and those behind it are sectarian bigots.
"It should never have happened and whoever is responsible will not succeed in driving a wedge between the good community relations that exist in the town."
Police called on anyone with more information to come forward.
© UTV News