Learn Farsi: نزدیک بود که رمز حساب بانک من لو برود. - The password to my bank account almost got exposed.

The phrase نزدیک بود که (literally "it was close that") establishes the past tense context. In Farsi, when you describe an action that almost happened using this phrase, the following verb takes the present subjunctive. You are essentially saying that in the past, the action was pending or hypothetical.

What is the infinitive of لو برود and how does it work?

The infinitive is لو رفتن (lo raftan), which means "to be exposed," "to leak," or "to be given away." It is an intransitive compound verb. If you want to talk about someone actively exposing or betraying a secret, you would use the transitive version: لو دادن (lo dādan).

How does the Ezafe link the words in رمز حساب بانک من?

This is a classic Ezafe chain linking four words together to show possession and specification. You add the invisible "-e" sound to connect each part: ramz-e hesāb-e bānk-e man. It translates literally as "password of account of bank of me."

Is the word که (that) strictly required after نزدیک بود?

No, in spoken and informal Farsi, the conjunction که is very often dropped. You will frequently hear sentences like this spoken without it, often combined with colloquial pronunciations like نزدیک بود رمز حسابم لو بره.