The Lafayette lawyer overseeing BP’s multibillion-dollar Gulf of Mexico oilspill settlement plans to resume paying some business claims next week after a federal judge in New Orleans this week lifted a temporary injunction that prevented him from doing so.

Starting Monday, Patrick Juneau said, his claims facility will begin processing claims for businesses that received an eligibility notice before Oct. 3, provided that the claimant has submitted final paperwork.

An eligibility notice says a company that claims it lost money after the spill has been approved for payment under the settlement.

BP has filed an application to prevent Juneau from paying such claims while it asks the U.S. Supreme Court to review a lower court’s ruling on the interpretation of the 2012 settlement. If the Supreme Court agrees to do so, that would stall Juneau’s plans.

Processing business claims that received an eligibility notice after Oct. 3 will require more time, Juneau said, because those claims need to be reviewed under a new policy that uses a formula to match a business’ revenue with expenses in showing post-spill losses.

It’s unclear how many claims are currently in the queue, said Nick Gagliano, a spokesman for the claims center.

The 2012 settlement was intended to avoid piecemeal litigation by resolving hundreds of thousands of claims for economic damage from what is generally considered the worst environmental disaster in U.S. history.

U.S. District Court Judge Carl Barbier, who is overseeing the litigation stemming from the 2010 Deepwater Horizon disaster, on Wednesday lifted a temporary injunction against payments of certain business claims. Barbier had issued the injunction in December at the direction of the U.S. 5th Circuit Court of Appeals.

The federal appeals court decided last week by an 8-5 vote not to reconsider an earlier decision upholding Barbier’s ruling that the settlement’s terms meant even unharmed plaintiffs could receive money and that BP knew as much when it agreed to the deal. BP has argued in court filings and ads that businesses should not be paid unless they can show the spill actually caused their losses.

Eleven men died when the Deepwater Horizon drilling rig caught fire and exploded April 20, 2010, about 50 miles off the Louisiana coast. Millions of barrels of oil poured into the Gulf of Mexico, into wetlands and onto the beaches of the Gulf Coast.

Follow Richard Thompson on Twitter, @rthompsonMSY.