Our level 3 party wiped the floor with the dragon in lost mines. It got off a breath weapon but died before it even got a second attack or movement.
So just don't look at numbers when describing expectations. It was one of the easiest fights we had. Yes we burned resources more because it WAS a dragon but smite, etc and it died.
If it got off to fly on its turn, etc it might have changed that. We were surprised because we said "we're dead" but 5e and damage can really make CR wrong based on circumstance
Did you fight the twig blights (or whatever they were called) before fighting the dragon?
A small village with multiple fights, and the dragon was oblivious to it all? The Passive Perception of the green dragon is something like 17. How the heck did your PCs get so close without alerting it?
Why didn't the dragon fight from the air where the PC's attacks are lessened? Why didn't the dragon's 40 hit point breath weapon kill some of the PCs?
Nearly 140 hit points in a single round by 3rd level PCs sounds extremely suspect. Maybe your DM lowered the hit points and breath weapon damage of the dragon, but I suspect that minimally, the DM did not run the dragon to its full perceptive, intellectual, and damage capacity. Lots of fights are easier if the DM does not run the NPCs to their potential or outright lowers the capabilities of the creature.
Not that I don't believe you, but I think your DM threw you a bone and you didn't fight the actual creature in the module. With 5 PCs, each 3rd level PC averaging 28 points of damage sounds really suspect, even if the Dragon lost initiative and the PCs all got two rounds of attacks off before the dragon got 2 off. The dragon has a high AC (18) and I find it unlikely that the PCs did 10 attacks against it and they all hit and that all of the attacked PCs saved against the breath weapon. For 3rd level PCs, the odds of 10 +5 vs. AC 18 attacks hitting are about 1/10,000 and the odds of say 3 PCs with +2 average to con saves all making their saves against DC 14 are 9%. Granted, a party wizard could be using magic missile and that would lower the odds to 6.5/10,000, but then again, the wizard would be doing below average damage and some other PC would have to pick up the slack.
Sorry. I don't buy that. Your DM fudged the encounter which is what I suspect that many experienced DMs did. Unlike the module designers, many experienced DMs are not stupid enough to put a near TPK into their games.
I would buy that a party of 3rd level PCs winning initiative could drive off the dragon when it got to half damage, but I don't buy that any group actually killed it without the DM fudging it. Having all of the PCs still conscious after the breath weapon alone should rarely occur.