This is the 455th most frequent Icelandic word.
lífi
"Lífi" means "life" in English.
In this sentence, "lífi" is the dative case form of the noun "líf" (life), used as the object of the preposition "í" (in).
Hún finnur gleði í daglegu lífi.
She finds joy in daily life.
Here, "lífi" is again the dative case, used with "í" to express the state of being in someone's life.
Vera í lífi einhvers er dýrmætt.
Being in someone's life is precious.
The term "lífi" is used in the dative case to indicate the circumstance (at risk to his life) in a general descriptive context.