Immuni means "immune" in English. It's an interesting word choice in a love song, as it's more commonly associated with health or legal contexts.
In "Amami Adesso," the artist uses it metaphorically to express a deep, enduring love that protects the couple from external troubles. They sing, "Insieme resteremo immuni alla sorte / Della crisi dei governi / Delle cose da comprare" (Together we will remain immune to fate / To government crises / To things to buy), suggesting their love makes them resilient against life's challenges.
Giordana Angi starts from a long view: "Tra cent'anni non ci ricorderemo / Degli sbagli di domani" (In a hundred years we won't remember / The mistakes of tomorrow). If today's errors will be forgotten anyway, the only sensible answer is "E allora sorridi" (So smile), and the plea that names the song, "Amami, amami, amami adesso" (Love me, love me, love me now).
The second verse lists what time will erase, "Della crisi dei governi / Delle cose da comprare" (The crisis of governments / The things to buy), against what will last: "Dell'amore che ci lega" (The love that binds us). In the chorus she pictures the two of them a century on with "un corpo solo" (one body), living in each other's smile and "immuni alla sorte" (immune to fate).