Armer was named among the substitutes for United’s 2-0 Champions League defeat to Atlético Madrid. The experience brought him into the senior European environment after he captained the Under-18s to the FA Youth Cup final last season.
Lawrence said seeing academy players reach that level was central to the club’s development pathway.
“Obviously, that's what it's all about, to see Academy players that have come through the Academy programme on that stage, in terms of playing or being in the squad at the highest level.
“And then being around the squad, to learn how they prepare and see the internationals, experienced players, going into that game and being part of that squad is obviously amazing.
“So it's a great opportunity for any of those individuals that are involved, for sure.”
Speaking to Manchester United’s official media, Lawrence said Armer’s progress over the previous 18 months to two years had not come as a surprise to staff at Carrington.
“Listen, like for anyone within the building, in terms of Dan Armer, he is, as a character and a personality, someone that really maximises his time in the building and the programme.
“And then, to be honest, we're not really surprised in terms of the progress he has made in the last 18 months to two years because we've always had a real belief in his qualities.
“When you do work with a player, you can see that he's hungry and he's fully invested in his development. There are obviously things that he's still working on and he still wants to push to improve. But he's someone who we've got good hopes for and, if he keeps developing in the way that he is at the moment, hopefully it's exciting for the future, in terms of his level.”
Armer turns 19 next week and could return to Under-21 action against Nottingham Forest, with the Premier League 2 fixture scheduled for Friday at Loughborough University. His recent appearances in victories over Ipswich, Leicester City and Brentford have provided further opportunities to progress, while the Champions League trip offered a different kind of education.
Lawrence’s comments make clear that United see the senior call-up as a developmental step rather than an end point. Armer’s task now is to keep improving the areas of his game that still need work and turn the experience into further progress.