A large crowd, some wearing masks and some carrying weapons, appeared on the streets of the area in sinister scenes.
The trouble is understood to be related to a feud within the UDA over ownership of a number of bonfires.
Mr Lyons said those behind the trouble had let Carrickfergus down at a time the town was paying tribute to its war dead.
"I utterly condemn the disorder," he said.
"I, along with many others, had been at the castle for a service of remembrance for the Battle of the Somme when news filtered through that these activities were taking place in Castlemara. The people of Carrickfergus do not want to see these sorts of activities, and particularly not as we gather to remember those who gave their lives for their country at the Battle of the Somme.
"It makes it all the more disappointing that these sort of things were going on."
The Fire Service was called to tackle a blaze close to the site of the estate's bonfire, while items collected for it including furniture, pallets and crates were scattered across a road, blocking access.
PSNI officers dressed in riot gear moved in and faced down the crowds.
Police have charged a 46-year-old man with riotous behaviour and a 36-year-old man with causing a dangerous article to be on a road.
Both are due to appear before Belfast Magistrates Court on July 28.
Superintendent Emma Bond said some of the men were armed with weapons including hammers.
Officers dispersed the crowd and seized a number of items, including a crossbow.
The disturbances came just two days after a man was shot in both legs in the same area. The paramilitary-style shooting took place at a house in Dunluskin Gardens.
Mr Lyons said police have assured him that resources were in place to keep the situation in order, and he urged people to keep cool heads.
He added: "We were at a place that people do not want to see. I would urge people to stay calm and think about what they are doing - this sort of thing is not on."