Both of these cases are similar in that both clarify the circumstances in which the prosecution in a capital case may remove jurors from the jury pool because they oppose the death penalty. Witherspoon was a 1968 case that made it harder to remove such jurors while Lockhart was a 1986 case that made it somewhat easier.
In Witherspoon, the Court held that a state could not make a law that would allow prosecutors to remove any juror who expressed opposition to the death penalty. The prosecutors would have to probe the person's opinions to see if they might apply the death penalty even though they were opposed to it. In Lockhart, the Court held that jurors could be removed if they said that they would never vote for the death penalty under any circumstances.
So, both cases work to clarify when prosecutors may remove prospective jurors for cause in capital cases. Witherspoon made it harder to do so while Lockhart made it somewhat easier.