It follows a disastrous summer for the airline with numerous delays and cancellations affecting passengers region wide.
One petition named HOLD LIAT Accountable has 415 signatories while a Facebook group for the petition has over 1,500 members.
Another petition calls on the prime ministers of three of the four shareholder governments – Freundel Stuart from Barbados, Baldwin Spencer from Antigua and Barbuda, and Dr Ralph Gonsalves from St Vincent and the Grenadines – to get rid of the entire board and the top management within six months.
Further, the petition calls on the government leaders “to reduce and remove all airport, airline and passenger travel taxes fees and charges imposed by shareholder governments.
LIAT CEO Ian Brunton has defended high regional airport taxes. He says they are needed because there is not enough traffic going through the airports to cover the cost of running an airport.