It happened shortly after 1:00 Wednesday morning, behind the Wash 'n Dry Laundromat, near 49th and Avenue Q.
Lubbock police say they tried to approach two suspects for what they call "suspicious" activity.
One suspect ran off, but police quickly caught and arrested him.
The other suspect continued running and pulled a gun on the officer.
That's when he was fatally shot by an officer.
The names of those involved were not released as of 7:00 this morning.
This is the second officer involved shooting in Lubbock this month.
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