Learn Turkish: Babamın berbere gitmesi lazım. - My father needs to go to the barber.

In this necessity structure, you are literally saying "My father's going is necessary." Because we use the possessive ending -si on the verb (gitmesi = his going), the person doing the action must be in the genitive (possessive) case. That is why we add -ın to make it Babamın.

Break down the grammar of gitmesi lazım for me. How does it mean "needs to go"?

This is the standard way to say someone "needs to" or "has to" do something in Turkish. You take the verb root git (go), add the short verbal noun ending -me (making it "going"), and then add the possessive suffix -si (his). So gitmesi means "his going". Add lazım (necessary), and you get "his going is necessary" — or, in natural English, "he needs to go".

Why is there an -e attached to berber?

The -e is the dative case suffix, which shows direction and translates to "to". Verbs of motion like gitmek (to go) require the destination to have this ending. So berbere means "to the barber".

Can I use gerek instead of lazım in this sentence?