Lighthizer would first need to reach a preliminary finding of unfair practices by China before opening a formal investigation, which could take as much as a year, administration officials said.
Beijing issued the order on Monday.
Trump has said he would be more amenable to going easy on Beijing if it were more aggressive in reining in North Korea. "This is just the beginning".
The investigation could take up to a year, according to administration officials, opening the door to a settlement before a possible investigation is launched.
In a phone call Friday, Trump praised Chinese President Xi Jinping for backing the recent United Nations vote to impose tougher sanctions on North Korea, and the leaders reaffirmed their commitment to a nuclear-free Korean Peninsula.
Both declined to be identified as they are not authorised to speak to the media.
The UN sanctions, introduced to punish North Korea for its missile and nuclear programmes, do not include any bans on textile exports.
In one of his first actions as president, Trump in January formally withdrew the US from the Trans-Pacific Partnership trade deal. "But Washington will turn a blind eye no longer".
Despite Monday's expected action, Trump has so far refrained from making good on threats of retaliatory trade measures against China.
The Obstructionist Democrats have given us (or not fixed) some of the worst trade deals in World History.
Trump Condemns ‘Repugnant’ Hate Groups After Va. Violence
While Beijing has promised to open more industries to foreign companies, it also has issued new rules on electric auto manufacturing, data security, internet censorship and other fields.
"I think China can do a lot more (about North Korea)".
"There's always a possibility of smugglers, but I think the government and state-owned companies and lawful private sector business will generally implement the government's orders".
China, the isolated North's main trading partner, has been reluctant to push leader Kim Jong Un's regime too hard for fear it might collapse. But Beijing is increasingly frustrated with Pyongyang and joined in approving a U.N. Security Council ban on August 5 on coal and other key goods.
The Chinese customs agency said it will stop processing imports of North Korean coal, iron and lead ores and fish at midnight on September 5.
"After that, entry of these goods will be prohibited", said an agency statement. Xi, in his phone conversation with Trump, urged calm, the officials said. That should have made the White House happy, as China is one of the only countries that will trade with North Korea (above board, that is).
The annual cost to the United States economy of several categories of IP theft exceeds US$225 billion (S$306 billion), according to a report this year by the IP Commission titled The Theft Of American Intellectual Property.
Trump has requested similar inquiries on trade, but the reports haven't been delivered on deadline.
"If the US uses Section 301 (of the Trade Act) to pressure China, countries in China's export chain, including the US, Japan and South Korea, would be affected", said Liu Ligang, Chief Economist for China at Citigroup.
Banner - UMC Tucson among 'Best Hospitals' in US
The Mayo Clinic in Rochester, Minn., ranked No. 1 on the " Best Hospitals Honor Roll ", and the Cleveland Clinic ranked second. A hospital with more national rankings in the 12 data-driven specialties outranks a hospital with fewer national rankings.