The council made the comment yesterday after the Canadian lawyer appeared on the United Front for Democracy against Dictatorship (UDD) rally stage on Saturday and recommended changes to Section 112 of the Criminal Code, which deals with insults against the monarchy.
The LCT called on authorities to investigate the comments made by Mr Amsterdam, who is the lawyer of former prime minister Thaksin Shinawatra.
Speaking to the red-shirt rally on Utthayan Road on Saturday, Mr Amsterdam accused the Democrat Party of using the lese majeste law to suppress free speech and to stifle the public debate necessary in a democratic system of government.
The LCT labelled the comments inappropriate, saying it wanted to inform the authorities and the public about the proper conduct of lawyers and stressed that foreign nationals must comply with domestic laws.
Mr Amsterdam must be asked whether he clearly understands the offences he has potentially committed against national security, the LCT said.
It said Mr Amsterdam almost certainly committed security-related offences, and recommended a probe be launched into whether he intended to violate the law by making the comments.
Mr Amsterdam should also be investigated to determine what benefits he was gaining from representing Thaksin, it said.
The LCT also urged labour officials to help clarify whether Mr Amsterdam had entered the country on a tourist visa or had obtained a proper work permit.
If he was paid or had his expenses covered by Thaksin to speak at the rally then he must have a legitimate work permit, the LCT said.
Police and labour officials could be at risk of dereliction of duty if they choose to ignore a criminal offence, the union added.
The LCT said Section 112 of the Criminal Code is aimed at protecting the monarchy and those who violate it are breaching national security.