Who says "Tzam'ah Nafshi"?
Rashi: Keneses Yisrael, in Galus Bavel.
Why does the verse discuss thirst for water?
Radak: Ayalim thirst more than other species, and the desire of one thirsty for water is greater than that of one hungry for food. A person could not live for two or three days without food, but not without water. When he is thirsty for water and drinks, his Nefesh returns to him. The thirst of the intellectual Nefesh for its honor, is greater than the body's physical thirst for water.
Malbim: The yearning [for Giluy Shechinah, Nevu'ah and Ru'ach ha'Kodesh] is for two reasons. (a) It is natural, like an Ayal's thirst for water. My Nefesh, due to its nature, yearns for Elokim. (b) There is thirst due to an event, just like an Ayal has extra thirst after eating poisonous roots. So I felt.
Why does it say "l'Kel Chai"?
Radak: Yisrael are exiled among the nations; their gods are dead.
Malbim: The vitality of the Nefesh and its spirituality depends on Hashem - "v'Atem ha'Devekim ba'Shem Elokeichem Chayim Kulchem ha'Yom" (Devarim 4:4).
When will he see Pnei Elokim?