The Italian made him an offer he couldn't refuse so he had to give up his house ;)
I just can't make sense of this sentence. Should the 'lo' be 'gli' since 'the house was offering this to him'?
Duolingo's point is in the idiom "on the house"; that pronoun changes the intended meaning a bit.
- Questo offriva la casa: This is what the house was offering
- Questo gli offriva la casa: This is what the house was offering to him
- Questo lo offriva la casa: This was on the house (it was free / a homage).
The personal pronoun after the demonstrative pronoun doesn't seem correct when analyzing the sentence, but it's used quite a bit to stress the subject: "questo lo dici tu" (this is what you say / this is only your version), "questa pagina la leggo io" (I am going to read this page / leave this page to me).