Learn Hardcore Turkish: Yağ yemeklere lezzet katar.

Because yağ is the subject of the sentence. In Turkish, the subject normally appears in the nominative (no case ending). The verb katar agrees with this nominative subject.

Why doesn’t lezzet take the accusative suffix -i if it’s the direct object?

In Turkish, a direct object only takes the accusative -i when it’s definite or specific. Here lezzet (“flavor”) is indefinite (we’re talking about flavor in general), so it stays in the bare nominative form even though it’s the object of katmak.

What do the endings on yemeklere mean?

yemek = “food” or “dish”

-ler = plural, so yemekler = “foods” or “dishes”
-e = dative case, “to” or “for”
Together yemeklere means “to (all) foods” or “to (various) dishes.”

What tense or aspect is katar, and why is it used here?

katar is the Turkish aorist (geniş zaman) form of katmak (“to add”). The aorist in Turkish often expresses general truths, habitual actions, or universal facts. Since the sentence states a general fact—“Oil adds flavor to foods”—the aorist is the appropriate choice.

Is the word order fixed? Could you rearrange the words?

Turkish word order is relatively flexible, but the unmarked (neutral) order is Subject–Indirect Object–Direct Object–Verb:
yağ + yemeklere + lezzet + katar.
You could say for emphasis:
“Yemeklere yağ lezzet katar.”
or even
“Yemeklere lezzet yağ katar.”
—but the standard form keeps the verb last.

Why is yemek plural here? Could we say yemeğe instead of yemeklere?

Using the plural yemekler generalizes the statement to “all dishes” or “various foods.” If you mean “to the dish” or a specific food item, you could indeed say yemeğe lezzet katar (“adds flavor to the (one) food/dish”). But as a broad statement about cooking, the plural is more natural.

How would you say “Butter adds flavor to foods” in Turkish?

Replace yağ with tereyağı (“butter”):
Tereyağı yemeklere lezzet katar.