No you do not really need a high chair for a baby to eat.
But having a high chair helps out a lot and they are well worth the money since you can strap your baby into the high chair and then feed them or allow the baby to eat on their own easier which keeps them seated so that they don't get up and run around when they can and get choked.
Babies need a safe place to be fed and eat and a high chair is a great thing for that.
But you can hold a baby in your lap and feed them but it gets harder and you cannot easily get up and do something else but you still need to watch your baby when they are in the high chair but they do help a lot.
I would always recommend buying a high chair for your baby as they are really a good thing to have.