Lamb prices could reach $5 a kg within the next five years, Westpac economists believe.
Doug Steel said in the latest Agribiz newsletter that stronger world prices would drive up lamb prices from 383c a kg last season to average 439c a kg this coming season.
Beef was picked to rise from 316c a kg to 336c a kg over the same period.
But the prime lamb market could be about to make a significant and permanent improvement.
The lack of lambs, growing demand and higher grain prices pushing up the price of pork and poultry would result in what Mr Steel called "a permanent step up".
"Over the next five years, average lamb prices are expected to nudge $5 a kg. Beef prices are also expected to rise."
Mr Steel said United Kingdom lamb prices were 34% higher than a year ago and United States beef prices were 21% higher.
Red meat had been slow to respond to rising food prices internationally, because markets reacted differently.
The Australian drought, for example, had devastated milk production but resulted in more sheep being put on the market.
In the past three years, Australian sheep numbers had fallen by 15 million, or 15%, which had driven up sheep meat exports by 16%.
"More supply brought lower international prices," Mr Steel said.
Equally, subsidy changes in Europe had forced some farmers to destock, causing increased sheepmeat supply but resulting in a 10% decline in the United Kingdom flock alone.
But Mr Steel said it did not necessarily translate that higher international prices would feed back to farmers.
Farmers needed to capture those higher prices paid by consumers.
"Establishing a mega-company may well improve the chances of getting a better slice of the action."
Farmers and meat exporters could also benefit from the rush of countries seeking free trade agreements with New Zealand, in part, to secure food supplies.
Blotting the horizon were tight winter feed supplies and rising costs for fertiliser and fuel, which show little sign of easing.