Correct English would be, "We need a house in which to live.". As it stands, 'We need a house to live.", this implies we don't want a dull, boring house, but one that is full of life, lively, something going on regularly. I agree with nisennenmondai that, We need a place to live" would probably be a better translation of the intended meaning, although "house" can be a humble little one-family hut or mansion.
There is nothing wrong with "We need a house to live in". I get that lots of high school pedantic teachers who don't bother researching actual English linguistics will say you can't end sentences in a preposition, but in reality that's just trying to make English more like Latin. Prepositions have been used at the end of sentences in English for centuries and by the best writers. "We need a house in which to live" is certainly correct, but that doesn't make "We need a house to live in" incorrect.
The sentence potentially has a very different meaning without "in" at the end, because the suggestion is that without a house we will die. I also firmly agree with those who say that there is nothing wrong with ending a sentence with a preposition. "Language in use" is a far better basis on which to pursue language learning than strict, and in many cases outdated, grammatical rules.