It comes after Sinn Fein held a protest outside Bank of Ireland HQ in Belfast following the decision of the bank to drop the Irish facility on their ATMs due to lack of demand.
Mr Lunn said such protests needed to end if those from non-traditional backgrounds were to support the language.
“Alliance supports a realistic and proportional Irish Language Act as a way to celebrate our shared cultural heritage, not as a pre-condition for Government but to help create a stable form of devolution. But attempts such as this to police the private sector cross an important line and will not help build confidence in the wider community.
“For those who would not traditionally support the Irish language, this will do nothing other than raise the spectre of an Irish language police, when more should be being done to help encourage them to see the positive side of an Act.
“Alliance will continue to push proposals in discussions with all parties and interested stakeholders towards a workable solution which enables an Irish Language Act to be introduced for all in Northern Ireland.”