I suspect that President Trump deliberately used the word "lynching" in a tweet to describe the efforts to impeach him, knowing that it would evoke hysteria from Democrats accusing him of racism.  Lest I be accused of attributing to him mastery of 3-dimensional chess, it doesn't take a mastermind to understand that the media and other Democrats will take any bait at hand to accuse Trump of nefariousness.  The word "lynch" has roots far predating the Reconstruction period, during which the KKK, the paramilitary arm of the Democratic Party, summarily executed by hanging many freed slaves, as well as many white Republicans who supported Reconstruction measures, as even the NAACP acknowledges.  Lynching continued into the 20th century.  Leo Frank, a Jewish factory superintendent, was kidnapped from prison in Georgia in 1915 and lynched by a mob of citizens, none of whom were ever charged.

If we are going to natter on and on about "insensitivity," how about insensitivity to the white people, including Jews, who have been victims of lynching?

But I don't think linguistic history was Trump's motive; rather, it was the expectation that Democrats would condemn the use of the word as "racially insensitive," allowing the trap to be sprung.  For the history of Bill Clinton's impeachment reveals that the word was liberally employed by Democrats at that time.  Current House Judiciary chairman Nadler, for instance (via Breitbart):

According to an October 4, 1998, Associated Press article that touted Nadler's role as a top Clinton defender, the then-51 year-old congressman said:

I am the president's defender in the sense that I haven't seen anything yet that would rise, in my opinion, to the level of impeachable offense. …

I wish we could get this over with quickly. … In pushing the process, in pushing the arguments of fairness and due process the Republicans so far have been running a lynch mob.

CNN, in a burst of honesty, dug up its own tape of Joe Biden:

In an appearance on CNN in October 1998, however, Biden said the impending impeachment proceedings against then-President Bill Clinton could be viewed as a "partisan lynching."

"Even if the President should be impeached, history is going to question whether or not this was just a partisan lynching or whether or not it was something that in fact met the standard, the very high bar, that was set by the founders as to what constituted an impeachable offense," Biden said.

CNN carefully noted that Biden apologized in a tweet 21 years later:

This wasn’t the right word to use and I’m sorry about that. Trump on the other hand chose his words deliberately today in his use of the word lynching and continues to stoke racial divides in this country daily. https://t.co/mHfFC8HluZ

— Joe Biden (@JoeBiden) October 23, 2019

Biden seems to be admitting that he doesn't choose his words carefully, and finds it somehow offensive that another person chooses his words "deliberately."  Is he reckless and proud of it?

Mary Margaret Olohan of the Daily Caller News Foundation found other Democrats using the L-word back in 1998:

Multiple representatives compared Clinton's impeachment to a lynching, and several others condemned it as a Republican attempt to remove Clinton from office.

Democratic Illinois Rep. Danny K. Davis condemned the impeachment trial as "a lynching," and former Democratic Rhode Island Rep. Patrick J. Kennedy called it "a political lynching."

Faced with a media structure intent on driving him from office, President Trump's meta-strategy is to discredit the media and other Democrats as hysterical haters who are unfair and criticize him for the very behavior they engage in.  I hope he springs the trap today, on Twitter and at his rally in Pittsburgh.