Learn Hardcore Indonesian: Lusa pagi saya akan berangkat ke bandara lebih awal. - The day after tomorrow morning I will depart for the airport earlier.

Both are understandable. The default, most natural order is lusa pagi. You may see pada pagi lusa (with pada) in more formal writing, but in everyday speech people usually say:

besok pagi, kemarin malam, lusa sore, nanti malam (day + time-of-day).

Is akan required to talk about the future here?

No. The time expression already marks the future. Variants:

Lusa pagi saya berangkat ke bandara lebih awal. (very natural in speech)
Lusa pagi saya akan berangkat… (neutral/formal, a bit more deliberate)
Lusa pagi saya bakal berangkat… (informal)
Lusa pagi saya mau berangkat… (intention/plan; can sound like “want to”)

What’s the difference between berangkat and pergi?

berangkat = to depart/set off (often scheduled or from a starting point). Example: Kereta berangkat pukul 07.00.
pergi = to go (general movement). Example: Saya pergi ke bandara sekarang. In your sentence, berangkat ke bandara emphasizes the act of setting off for the airport; pergi ke bandara is also fine and neutral.

Why is it ke bandara, not kepada bandara?

ke is for movement to places: ke bandara, ke rumah.
kepada is for recipients (usually people): kepada Ibu Rina, kepada mereka. So kepada bandara would be wrong for physical movement.

Where can I put the time phrase and lebih awal in the sentence?

Indonesian allows flexible placement for time adverbials. All of these are natural:

Lusa pagi, saya akan berangkat ke bandara lebih awal.
Saya akan berangkat ke bandara lebih awal lusa pagi.
Saya lusa pagi akan berangkat ke bandara lebih awal. Keep lusa and pagi together as a unit, and place lebih awal near the verb or at the end.

What exactly does lebih awal imply? How is it different from lebih cepat, lebih pagi, and lebih dahulu?

lebih awal = earlier than expected/than usual/than scheduled (focus on time). Example: Berangkat lebih awal dari biasanya.
lebih pagi = at an earlier time of the morning. Example: Kita berangkat lebih pagi besok.
lebih cepat = faster (speed), not earlier time; avoid it here unless you truly mean moving faster.
lebih dahulu = before someone/something else (sequence), not necessarily earlier clock time. Example: Saya berangkat lebih dahulu, ya.

How do I say “very early”?

Use the idiom pagi-pagi sekali. Example: Lusa pagi-pagi sekali saya akan berangkat ke bandara.
For pre-dawn, use dini hari: Lusa dini hari saya berangkat…

Can I omit pagi?

Yes. Lusa saya akan berangkat ke bandara (lebih awal). That means “the day after tomorrow” without specifying morning. If you want to stress it’s in the morning, keep pagi.

Should it be ke bandara or di bandara?

Movement to: ke bandara (to the airport).
Location at: di bandara (at the airport). Examples: Saya akan berangkat ke bandara. / Saya sudah di bandara. / Saya akan tiba di bandara.

Do I need an article like “the” before bandara?

Indonesian has no articles. bandara can be definite by context. To be explicit, use a demonstrative or a name:

ke bandara itu (to that airport)
ke Bandara Soekarno–Hatta

Is bandara the same as bandar udara?

Yes. bandara is a contraction of bandar udara and is the common word for “airport”. lapangan terbang is more Malay/older style and less common in Indonesian today.

Can I use aku or gue instead of saya?

saya: polite/neutral (safe with strangers and in formal contexts).
aku: informal/intimate among friends/family.
gue/gua: very informal Jakarta slang. Example: Lusa pagi aku akan berangkat ke bandara lebih awal.

How do I add an exact time? Should I use jam or pukul?

Both work; pukul is a bit more formal.

Lusa pagi pukul enam saya akan berangkat ke bandara.
Lusa pagi jam enam saya akan berangkat ke bandara.

How do I make it negative?

Put tidak before the verb phrase (often before akan):

Lusa pagi saya tidak akan berangkat ke bandara.
Saya tidak berangkat ke bandara lusa pagi.

Do I need pada before a time expression?

No. pada is optional and more formal. You might see Pada lusa pagi saya akan… or Pada pagi lusa… in writing, but in speech people usually omit pada.

Any quick pronunciation tips for berangkat and lebih?

berangkat: ng is the single nasal sound [ŋ] as in English “sing”; don’t insert a hard “g”. The r is a tapped/trilled r.
lebih: pronounce the final h in careful speech; in casual Jakarta speech it may be softened or dropped.