I can't find any real quote from a defence department official stating what Lakhota claims was stated.
There are claims it was stated, but no quote, and no names. Like this...
F-22 Safely Shoots Down Chinese Spy Balloon Off South Carolina Coast
A U.S. Air Force fighter safely shot down a Chinese high-altitude surveillance balloon, Secretary of Defense Lloyd J. Austin III said in a written statement.www.defense.gov
The link above seems to insinuate that Secretary Austin said it, but that does not seem to be true.
Here is Defense Secretary Austin's statement...
Statement From Secretary of Defense Lloyd J. Austin III
Secretary of Defense Lloyd J. Austin III issued a statement on the downing of a high altitude surveillance balloon launched by and belonging to China.www.defense.gov
No mention of it occurring under Trump.
Other news reports claim "According to a senior defense department official." Those are normally BS, made up by some reporter who spoke with a janitor.
Please provide an official source for the statement Lakhota. Tweets don't count unless they come from the DOD. Thanks.
An unnamed Pentagon official, reported from a reliable source, is all I need.