(今電話で話してた)あの男が君に今日昼食をご一緒しませんかって S asking if

That was the man asking if you could have lunch with us today.


伝聞のシンプル化(文法跳躍)

that was S (and S was) asking if...


あなたが (O を) Vできるかどうか伺う

ask if you could V (O)