In the passage: It was only with the growth of paediatrics and psychology in the 20th century that studies could be carried out on a more objective, if still not always very scientific, basis.
In the questions: "19th century studies of genius lacked both objectivity and a proper scientific approach" is true.
My thinking: It writes "more objective" and "still not always very scientific" in the passage which, personally I think, means that previous studies were objective and scientific, but not substantially, so the statement in the questions should be false.

太久不看英文了，看不懂了。

yet the word "lack" doesnt necessarily meam that previous studies were totally not objective and/or scientific,for "lack"refers to to be missing or just "deficient".......

I think the passage meant that the methods were always scientific, yet the previous approach lacked authority. The approaches now to the studies are more recognized hence more 'objective'.