Lieu is one of at least 16 Democrats who will not be attending the ceremony on Jan. 20. In a statement, he said it was a personal decision and that he doesn't dispute Trump's presidency.
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"Trump - who lost the popular vote - made a series of racist, sexist and bigoted statements," he said. "In addition, he attacked Gold Star parents, veterans such as John McCain and now civil rights icon John Lewis."
In a series of tweets, Trump said Lewis was "all talk" and "no action or results."
Lewis, who is a 16-term congressman and represents a portion of Atlanta, Georgia, said Trump's presidency was illegitimate because of possible Russian interference during the election. It was part of an interview set to air on Sunday for NBC's "Meet the Press."
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Lewis added that he would not be attending Trump's inauguration because of that, which is the first ceremony he will miss since joining congress 30 years ago.
The flurry of comments and responses come days before the national holiday honoring Martin Luther King Jr.
"For Donald Trump to say that John Lewis is 'all talk, no action' is not only historically just wrong, but it is really disparaging a civil rights icon," Lieu said.
Even Republicans lambasted Trump for his comments about Lewis. Nebraska Sen. Ben Sasse tweeted that Lewis's "talk" has changed the world.
Lewis suffered a skull fracture during the march in Selma, Alabama in 1965 and has devoted his life to promoting equal rights for African-Americans. Lewis is also one of the original Freedom Riders.
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Trump's assertion that Lewis' district is "falling apart" and "crime infested" is hard to prove.
Georgia's 5th Congressional District includes the Atlanta metro region, which has a large African-American population. The district is considered one of the nation's fastest growing areas, but its crime and poverty rates are higher than the national average.
The district has an 8.2 percent unemployment rate and the median household income is about $48,000, according to the Census Bureau.
Trump's transition team said the president-elect plans to visit the National Museum of African American History and Culture on Monday in observance of Martin Luther King Day.
The Associated Press and City News Service contributed to this report.