Cant we say the priminister is coming to have lunch with me, instead of going in this case?
That would be "statsministeren kommer for å spise lunsj med meg."
"Kommer til å" is a set phrase that means "is going to."
Please accept 'going to lunch with me'; it's perfectly acceptable as a verb in English. Thank you.
"the prime minster is going to have lunch with me" is just as acceptable in \English and more likely
In my nightmares! (in UK).