Taiwan now has diplomatic relations with only 18 countries.
The destruction of the nuclear sites is taking place in Punggye-ri where North Korea has tested at least six nuclear weapons.
The United States has withdrawn an invitation to China to attend a major US-hosted naval drill
Lu's comment came after US President Donald Trump on Tuesday hinted that his scheduled meeting with the top leader of the DPRK Kim Jong Un, originally set to be held on June 12, may be delayed.
Trump and Kim but the US president on Tuesday seemed to suggest the talks would be delayed indefinitely.
Kim had raised the stakes last week after the North Korean government declared that it would call off talks