Although Denmark controls the Arctic, there is a US military installation there as well as potential for mineral and oil mining.
Trump has brought up the subject numerous times during his first term as president and has recently refused to rule out using economic or military power to annex the region.
Trump’s words and deeds did not always align, Lammy said on BBC Radio 4’s Today program.
Greenland and its capital, Nuuk, are depicted on the map.
The most recent dispute started when Donald Trump Jr., the president-elect’s son, traveled to Nuuk, the capital of Greenland.
Danish Prime Minister Mette Frederiksen responded by telling Danish TV that “Greenland belongs to the Greenlanders” and that the future of the region could only be decided by the local populace.