First, the numbers
A group of 8 3rd-level adventurers have a budgeted XP threshold of 600, 1200, 1800, and 3200 for an Easy, Medium, Hard, and Deadly encounter.
A Young Green Dragon has an EXP value of 3900, which is Deadly. But! remember, you have to account for having more than the recommended player count of 4-6. The DMG goes off to say:
… If the party contains six or more characters, use the next lowest multiplier on the table. Use a multiplier of 0.5 for a single monster.
Therefore, for a group of 3 to 6 adventurers, the Young Green Dragon would be, theoretically, Deadly. But for a group of 8, it is only Hard. Like you, I have DMed LMoP for a group with more than the recommended players. I had 9 players fighting the Dragon at the time, and it was brutal (two of them fell unconscious, and their Donkey died- poor Will Smith) but they pulled it off.
Second, the numbers lie
Much of how difficult the fight turns out is how it starts and how the circumstances mount against or for the players.
If your players simply run in, guns blazing, it will more likely lead to a TPK, which, depending on your preference may or may not be a desirable outcome. If your players are smart about it, they can easily employ tactics that will turn the battle toward a favorable resolution. Or, they can find out more about the dragon and its strengths and weaknesses in order to be more prepared.
This is a broad discussion and I won’t delve into it in fear of getting too opinionated.
Thirdly, know your characters
Looking at your party, they all look pretty high-tier: moon druids, fighters, barbarians, and rogues are really strong at this level so you shouldn’t worry too much. Now, if the group were mainly composed of diplomat monks and courtly wizards who specialize in non-combat areas of the game, you’re going to have a problem.
Lastly, don’t forget this relevant text:
Warning! Spoilers! If you plan on playing LMoP, do not look
From page 33 of the module, it says:
Venomfang does not want to give up such a promising lair, but if the characters reduce the dragon to half its hit points, it climbs to the top of the tower and flies off to fight another day.
So your players are really only fighting half of the Dragon. Good luck!