What is the grammatical name and function of the sentence" the lifeline of another man

It is a noun phrase. This because a noun is being used here and it has a part of sentence having no finite verb.

noun phrase

Noun Phrase

Noun phrase

Noun phrase

Noun phrase

Noun phrase

Noun phrase

Are you guys sure of this answer, because you are not answering my question,you only answer the first one not the second one that is, function not only grammatical name and I am not asking the reason why it noun phrase, simple question simple answer

Noun phrase because it has no finite verb.

It functions as the object of the verb"continues".