Cesium is the most reactive element among the given elements (Cesium (Cs), Barium (Ba), and Lutetium (Lu)) because it has the lowest ionization energy and largest atomic radius. Cesium is located in Group 1 (alkali metals) of the periodic table, which are known for their high reactivity due to their tendency to lose their outermost electron (valence electron).

As you move down a group in the periodic table, the atomic radius generally increases. The larger the atomic radius, the weaker the attraction between the nucleus and the outermost electrons. This makes it easier for the outermost electron to be removed, resulting in a lower ionization energy.

Among Cs, Ba, and Lu, Cesium has the largest atomic radius and the lowest ionization energy. Therefore, Cesium is the most reactive element among these three elements.