Lawrence and Davies come into the squad for the away European Challenge Cup opener with Timisoara Saracens on Saturday (kick-off 12.30pm BST) for Richard Hibbard and Rhodri Williams.
And Jackman insists both fully deserve their opportunity after impressing on Celtic Cup duty in recent weeks with Dragons A.
“I’ve been very pleased with Rhys. He’s been working with two young props (in the Celtic Cup) and he has done a good job in terms of helping them,” said Jackman.
“He has been with two props we really like in Josh Reynolds and Chris Coleman and he deserves a crack.
“The beauty of that A competition is that he has been able to get game time all along. If we need him Saturday, he will have game time in his legs.
“Rhys gives us experience too. Last year, when Elliot (Dee) wasn’t there, we were using two young hookers.
“At hooker it is nice to have someone who has experience and set piece wise is composed. He gives us that.
“Tavis (Knoyle) will start but Rhodri (Davies) will come up,” added Jackman.
“We really liked what we saw of him in pre-season and he then had a niggle that knocked him out of the first two games.
“He has had two games in the Celtic Cup and Chappy (James Chapron) has been happy with him, we’ve liked what we’ve seen so it’s an ideal opportunity to re-integrate him.
“Rhodri is a game changer. He is incredible quick and powerful. Until he gets up to speed, it will be impact from the bench.
“He’s an ex-Sevens player, he scored a lot of tries last year for Rotherham and he will come on and help increase the tempo.
“He is dangerous around the breakdown, where it is important to have a nine who can snipe, particularly late in games. We’re excited to see him play.”
After Saturday's game in Romania, Dragons face a quick turnaround to take on Northampton Saints in Newport next Friday, kick off 7.30pm.
CLICK HERE to secure your tickets for the clash with the English Premiership opponents at Rodney Parade with early bird offer now available