Yes, you should lock your elbows at full extension for each completion of a bench press repetition and also the knees at the top of the squat.
This is supported by text from Starting Strength, 3rd Edition:
Regarding the bench: "...push up on the bar, locking out your elbows."
"At the top [of the squat], all the skeletal components that support the bar - the knees, hips, and spine - will be locked in extension so that the muscular components have to exert only enough force to maintain this position."
I will speculate as to some reasons for this:
- allows you to release your valsalva maneuver and take a breath of air while the weight is supported by skeletal components
- allows you to train through the full range of motion