Six Nations - Triple blow for Scotland
Full-back Southwell has not recovered from the facial injury he suffered in the defeat by Wales earlier this month.
Northampton centre Ansbro suffered concussion during his team's defeat by Bath at the weekend and Toulon full-back Lamont sustained a leg injury against Agen.
Scotland head coach Andy Robinson said: "We have made the decision now that all three of our injured backs will miss this weekend's international, so that brings clarity to our preparations.
"We wish all of them a speedy recovery. Our medical staff will continue to treat and monitor our injured forwards.
"Everybody was hurting after the display against Wales but we must now focus on the challenge that Ireland bring, and there's absolute determination to bounce back against them at Murrayfield on Sunday."
Six forwards sat out training on Monday, with Scotland team doctor James Robson reporting that they will require further medical assessment.
Glasgow Warriors pair Jon Welsh (ribs) and Robert Harley (hip), Edinburgh flanker Ross Rennie (toe) and Leinster lock Nathan Hines (knee) all suffered knocks in Magners League action at the weekend.
Richie Vernon is still feeling the effects of the calf knock he suffered against Wales, while hooker Dougie Hall continues to be troubled by the shoulder injury that ruled him out of the Murrayfield defeat.