They had until the end of November to submit an environmental report.
But now they have asked for an extra 11 months to supply it.
If the order was to be granted it would extend the appeals process.
The firms can continue extracting sand while the outcome is being decided.
The companies were ordered to stop taking sand from the bed of the lough in May.
The Department of the Environment (DoE) issued an enforcement notice because the work did not have planning permission.
About 1.7m tonnes a year are taken out using barges.
Environmentalists have said the extraction could affect bird habitats on the lough, which is an internationally recognised sanctuary with EU protection.
Solicitors for the sand companies said they have been unable to find out exactly what information the DoE wants in the environmental report.
They also said that bird surveys and food availability checks should be done over a full season, which includes next summer.
Green Party leader Steven Agnew is opposing an extension of the deadline and said sand traders had "known for many years that their activities need to be regularised".
"Little progress has been made in stopping unauthorised sand dredging on Lough Neagh to date and any further delay is unacceptable," he added.
The Planning Appeals Commission will decide whether to grant an extension.
It is expected to do so by late-October.
The extraction of sand from the lough has proven to be hugely controversial.
Earlier this month the environmental group Friends of the Earth said it was taking the DoE to court over Environment Minister Mark H Durkan's refusal to issue stop notices to the sand traders.
Unlike an enforcement notice, a stop notice cannot be appealed and can only be challenged in the courts.
Companies appealing an order to stop dredging sand from Lough Neagh are seeking a lengthy extension to a key deadline.