Does "and sent packing to" mean "and reduced to a position in"?

To be "sent packing" is an idiom meaning to be unceremoniously sent away or dismissed.

Thanks.
So he's sent away to the garrison in Europe to take another (minor) position?

He was not demoted, merely given a symbolic rebuke.

Doesn't Joint Chiefs chairman rank higher than a position in a European NATO garrison?

Lyman Louis Lemnitzer served as Chairman of the Joint Chiefs of Staff from 1960 to 1962. He then served as Supreme Allied Commander of NATO from 1963 to 1969. This did not involve a reduction in military rank, nor a loss of status. He was "shifted sideways" or maybe even "kicked upstairs" (ways of dealing with high ranking officials who have incurred displeasure where it would be undesirable to draw public attention to the matter).

Note the mis-spelling of "principal" in your original piece, widely repeated in the many 9/11 conspiracy-theory websites where it may be found.

The roles of Chairman of the Joint Chiefs of Staff and Supreme Allied Commander of NATO were both 4 star General appointments, thus no effective demotion took place. In fact Lemnitzer went on to hold other prestigious roles under successive Presidents. As of 2015, he is the only Chairman of the Joint Chiefs to hold another U.S military command after his term as Chairman ended, rather than retiring.

Excellent!

It is not certain that his move to Europe was a punishment. It is an allegation made by conspiracy theorists.