This movie is about... -SPOILERS!-
...Psychosis
I think this movie was about a young woman suffering from psychosis; nothing more, nothing less. We see 'reality' through her eyes and are left confused as to what is real and what is imagined. Some of what the viewer saw is real, and some is the fictional world as perceived by Lily during her psychotic episodes, and we're left unable to tell exactly where reality ends and where delusions dominate, as life is for those unfortunate souls who suffer from psychosis.
We're given some clues about this. At one point Lily is fighting off the children on the lawn (this is 'reality' from her perspective at this point), then in the next shot she is on the lawn by herself fighting off malevolent entities that simply don't exist, this is how an external observer would have seen her; totally demented and in the middle of a severe psychotic episode. Also, at one point we hear the old lady saying on the radio that Lily is deluded and thinks there is a war in progress etc; we can assume that Lily has overheard people saying this at some point, perhaps her family members saying this to each other or perhaps doctors in the mental institution that she presumably inhabits.
She also converses 'telepathically' on occasions. This suggests that some of the main characters in the movie are also non-existent, e.g., Brother Lily never says a word (if I remember this correctly) and it could be assumed that he is as 'real' as the unicorn; he simply doesn't exist. We're also given some 'real world' sources for some of her delusions, e.g., the painting of the hawk is the source of her delusion about the hawk and it's fate.
So I think the purpose of the movie was to provide the viewer with an insight into the life of a psychotic, and show us how impossible it is for those who suffer from severe psychosis to live a normal life with normal social interaction. Life for Lily is frightening, confusing and unpredictable and inhabited by malevolent entities intent on doing her harm.
The thing that bothers me most about this movie is the IMDb score; 6.0/10. I can only guess that many simply didn't 'get it'. I'm going to watch this again sometime in the next few days while it's still fresh in my mind.
Here's a Wiki link on psychosis for those interested.
http://en.wikipedia.org/wiki/Psychosis