A "full-court press" is a defensive move in basketball, which is a game that
is played on a marked area of floor called a court. In this case
"press" refers to the action of pressing, or pushing.
"Press"
also means a machine that prints words on paper, and by extension the
business of publishing. "The press" can refer to newspapers and the
people who work for them. "The power of the press" is a phrase
referring to the power that newspapers and magazines can wield over
others; for instance, exposing a scandal can ruin a politician's
career.
The quoted line mixes up these two phrases in a play on words. Lois doesn't just have "power" of the press---she has "full-court power."