Learn Hardcore Icelandic: Lykillinn hlýtur að vera í geymslunni, því ég setti hann þar í gær. - The key must be in the storage room, because I put it there yesterday.

-inn is the suffixed definite article in Icelandic (roughly “the”).
So lykill = “key” (indefinite), while lykillinn = “the key” (definite).
It attaches to the noun and triggers some spelling/ending patterns depending on the noun’s declension.

What does hlýtur að mean grammatically, and why is it used here?

hlýtur is the 3rd person singular present tense of hljóta. In this construction hlýtur að + infinitive, it expresses a strong inference/necessity (“must”, “is bound to”, “has to be (the case)”).
So Lykillinn hlýtur að vera... is “The key must be...”, often implying the speaker is concluding it based on evidence (e.g., “because I put it there”).

Why is there an að before vera?

After many verbs (including hljóta in this meaning), Icelandic commonly uses að as an infinitive marker, similar to English “to”.
So hlýtur að vera = “must to be” in structure, i.e. “must be”.

Why is vera in the infinitive form?

Because hlýtur is the finite (conjugated) verb of the clause, and the following verb stays non-finite (infinitive).
Pattern: finite verb + að + infinitive → hlýtur að vera.