Lancaster was appointed full-time national head coach last month after proving his worth with wins over Scotland, Italy, France and Ireland during his interim reign.
The former Leeds director of rugby is now working on formulating the makeup of his squad and backroom staff ahead of the summer tour to South Africa.
England haven't tasted victory against the Springboks in South Africa since 2000, suffering a whitewash in 2007, and Dallaglio insists Lancaster will face a true test of his credentials over the course of this summer's three-Test tour.
"South Africa is very tough and one of the hardest places to play rugby," he said.
"I think when they come away from there they will know what they need to do both on a player perspective in terms of the squad but also a coaching perspective.
"He certainly deserves the opportunity to continue in that role, there's no doubt about it.
"His record from the RBS 6 Nations shows how he has turned England's fortunes round in a very short space of time.
"Coaching at the highest level is not normally down to one person, it's down to a number of factors.
"Stuart and his team will know whether they need to add to that coaching staff at the end of the tour or if they've got enough themselves to do the job."