Learn Hardcore Korean: oneul jeomsimi maseobseosseoyo.

이 is the subject marker used after a noun ending in a consonant (here, 점심). It simply marks lunch as the grammatical subject: “(Today’s) lunch was not tasty.”
You can use 은/는 to make 오늘 점심은 맛없었어요, which adds a topic/contrast nuance: “As for today’s lunch, it wasn’t tasty (implying contrast with other meals or other days).”
You can also say 오늘은 점심이 맛없었어요 to make “as for today, (specifically) lunch was not tasty.”

Why can 오늘 appear without a particle? Should it be 오늘에 or 오늘의?

Time words like 오늘 commonly function as adverbials without any particle, so 오늘 점심이… is perfectly natural.
오늘에 is usually wrong here (it sounds like “at today”).
오늘의 점심 is grammatical but sounds written/formal; in everyday speech, 오늘 점심 is preferred.

Is 맛없었어요 past tense? Why is it -었- and not -았-?