Regulations state the defendant should have been at least 500 feet (152.4m) above the ground and the summary of facts noted the defendant's flight was "significantly below" that required level and in very close proximity to people and buildings on the ground.
When questioned in March, Lawrence was co-operative and didn't deny the behaviour, saying it was "excitement and stupidity".
He denied asking his son to deliberately film the low flight, implying it was not a prearranged stunt, and said he simply flew past.
He agreed there was an obvious danger to the people and property involved and was apologetic; describing himself as a "bloody idiot" and giving assurances he would not fly like that again in the future.
Defence lawyer James Rainger told the court his client had pleaded guilty at the earliest opportunity and didn't realise his son would jump out on to the beach.
Judge Max Courtney convicted and fined him $2000, ordering him to pay court costs of $130.
The judge noted he had flown "extremely low" with his feet at or below the concrete retaining wall that lined the beach.
The Haumoana man recently won an eight year-long battle with the Hastings District Council to keep the 40m seawall, built without consent and not complying with the building act, protecting two beachfront properties from the coastal elements.
The maximum penalty for operating an aircraft in a careless manner is a fine of $7000.