To the ones who say this is idiomatic: I think it's the other way around.
«It's on the house» literally means that something is on top of a house, though most people say it meaning, idiomatically, that the house offers something to someone for free.
On the other hand, «offre la casa» literally means that the house (bar, café, host, etc.) is offering something to someone, e.g. "la casa offre la birra (a te)".
To further stress my point, this is how the English expression "it's on the house" is said in other languages:
- Spanish: «Invita la casa» (lit. the house pays) or «cortesía de la casa» (lit. a gift from the house).
- French: «C'est offert par la maison» (lit. it's offered by the house) or «c'est la maison qui l'offre» (lit. it's the house who offers it).
The ability of inverting the subject with the verb and the object or even omitting it altogether in an Italian sentence makes this effectively impossible.
So "offre la casa" could actually mean either of these:
- She/he offers the house.
- The house offers. (i.e. it's on the house)
In order to rid this sentence of its ambiguity, you could respectively say:
- Lei/lui offre la casa. (explicit subject)
- La casa offre. (normal word order)
By normal word order I mean Subject-Verb-Object (SVO), as is the case with all Romance languages.
More on word order and implicit subjects:
I personally think that idioms are all very well if you know that they exist - perhaps a warning to "think laterally" or "this one's a bit outside-the-box" might help. Even then it's a bit daft when many people are trying to learn with limited additional resources - or, in my case, when the additional resources provide no help with idiomatic phrases.
Fascinating as an idiom might be once you know about it - i agree to that - it is quite frustrating and demoralising to many learners when they are used to trip you up. In this software it does feel rather like you're being set up when they appear out of the blue.
I am not a beginner in language learning - just a beginner in Italian - but I know that I don't like being given challenges that are impossible, whatever the circumstance.
Your idea is the perfect thing to spend lingots on (hence it also has the advantage of being optional). I really like the idea of offering on the lingots page some special functionality like having a little warning, like 'think laterally' (maybe there should be an image of the owl with one raised eyebrow ;-), or maybe even a direct warning that it is an idiom. I would give up some lingots for that, and I know they were looking for ideas on how to spend lingots in order to encourage even more learning.
I am a native English speaker. We would say It's on the house, doctors if we wanted to let the doctors know that stuff was free, or we are paying for it, or whatever.
'offer of the house, doctors' seems to me a reasonable interpretation, although we would never say that way in English. It seems close to some of the other languages listed above; like the way it would be said in French.