"Mi ha fatto" is literally "has made me", and it's a way to introduce a passive action: "la sola vista mi ha fatto svenire" (the sight alone made me faint). "Il mio fratello" is wrong (no article before one's family members in the singular!) while you'd need an article before pranzo, so it should be "mio fratello mi ha fatto mangiare il pranzo". Although that sounds as if your brother forced you to eat.
This is really useful as it is a pattern to use and recognise. "il mio fratello" - oh well. But I put 'pranzo' instead of 'il pranzo' on purpose. I have no real understanding of when you use the article beyond "more than in English". And yes, the intention was that the brother forced me to eat lunch :-)