the lifeline of another man what grammatical name is given to this expression and what is its function
The expression "the lifeline of another man" is an example of a noun phrase.
A noun phrase is a group of words that functions as a noun in a sentence. It typically consists of a noun (in this case, "lifeline") and any modifiers or determiners that provide further information or context (in this case, "the" and "of another man").
The function of the noun phrase "the lifeline of another man" is to act as the subject or the object of a sentence. It can be used to refer to a specific lifeline that belongs to or is associated with another man.