I know the epilogue to DH doesn't say this, but are there any interviews or other JKR info about which houses the Potter children were sorted into?
James was sorted into Gryffindor, Albus Slytherin, Lily unknown.
Today (1 September 2015), JK Rowling was tweeting about how James Potter II was making his first trip to Hogwarts. Naturally, this meant he was due for Sorting, and in the UK evening, she tweeted the results from the Sorting Ceremony:
Have just heard that James S Potter has been Sorted (to nobody's surprise) into Gryffindor. Teddy Lupin (Head Boy, Hufflepuff) disappointed.
A year later, with the publication of Harry Potter and the Cursed Child (i.e., the year when Albus actually went to Hogwarts), we learn that Albus was sorted into Slytherin.
At time of writing, there’s still no information about where Lily ended up – I’d expect we’ll find out in a few years, when the timeline matches her going to Hogwarts.
Well, there is no canon on this, in the books or otherwise, so I'll make a canon-based guess.
J.K. Rowling has established that families often go into the same house as their ancestors. Albus Severus was pretty dead set against going to Slytherin and Harry assured him that the Sorting Hat would take his wishes into consideration. Both Ginny and Harry were Gryffindors, as were Harry's and Ginny's parents respectively, as well as all of Ginny's siblings. I think Gryffindor makes the most sense.
Edited to add: I thought about this a little bit more and I can't help but wonder if any of Harry's children had more of a chance of going to Slytherin if it wouldn't have been James. While I won't go so far as to suggest James is a bully, he definitely gives Al a hard time at King's Cross and deliberately provokes Al's anxieties.
Further, J.K. Rowling has said that, although Harry wouldn't have outright given the Marauder's Map to any of his children, James would've been the child to find the map in Harry's desk and nick it. It seems clear from canon that James is a Gryffindor, but he seems to walk a little on the wild side, a trait that Slytherin prizes (for confirmation see "Is Slytherin Evil" here on SFF or Dobby's Reward in Chamber of Secrets where Dumbledore explains to Harry that Salazar Slytherin did prize "resourcefulness, determination, and a certain disregard for the rules.") Perhaps James had a close call with the Sorting Hat, like Harry, and was projecting his own fear of Slytherin onto Al by ribbing him. Again, just an idea, but one with canon in mind.
We really know nothing about Lily, except that she's two years younger than Al and can't wait to go to Hogwarts herself. There's nothing in the epilogue to really delve into what traits Lily has and what house they might qualify her for, so I'll stick with Gryffindor for Lily due to the family connections.
ETA: Harry Potter and the Cursed Child (released 07.30.16) clarifies that James and Lily Potter went to Gryffindor, while their brother Albus Severus went to Slytherin (w00t!).
According to Harry Potter and the Cursed Child, Albus Potter was sorted into Slytherin house.
ALBUS walks swiftly to the front of the stage.
SORTING HAT: Albus Potter.
He puts his hat on ALBUS’s head — and this time he seems to take longer — almost as if he too is confused.
There’s a silence.
A perfect, profound silence.
One that sits low, twists a bit, and has damage within it.
POLLY CHAPMAN: Slytherin?
CRAIG BOWKER JR.: Whoa! A Potter? In Slytherin.
Sadly, there is no canon info about this... yet. "Harry Potter and the cursed child" is a play, in which Albus Severus Potter's house will most likely be revealed.
Harry’s name in the title is the giveaway that Mr. Potter is in this play. It’s an official new story that picks up where the Deathly Hallows epilogue left off. Harry is an overworked Ministry of Magic employee, as well as a husband and father. The play will explore how Harry wrestles with his past and how his youngest son Albus Severus deals with the heavy burden of the family legacy. Now that does sound epic. This is also the very first time an official Harry Potter story has been presented on stage.
The only reason Harry could have been sorted into Slytherin was because the Sorting Hat recognised the part of Voldemort's soul attached to Harry's and the potential influence that could have had on him. Had this not existed he would have indisputably been put in Gryffindor.
Therefore, there is no reason for Harry Potter's children to be sorted into Slytherin - their parents naturally possess none of the traits of a Slytherin and both of their parent's families come from long lines of Gryffindors so they would almost certainly have all been sorted into Gryffindor.
I know many online fanfictions support the depiction of Albus Potter as a Slytherin, because it supports the post-war idea of inter-house harmony (many of them show Scorpius Malfoy as Albus Potter's friend). But realistically J.K Rowling would not have tied up all the ends quite so neatly - it's just not her style and is at odds with all of the information previously provided in the books. And anyway, if Albus Potter knew he could chose Gryffindor and was opposed to being a Slytherin, why would he not do what his father did and chose?
First off, James was obviously sorted into Griffyndor, because if he was a Slytherin Albus being sorted into it would not be such a big deal. Besides, JK has shown through McLaggen & the Weasley twins that some Griffyndors can certainly be bullies. Being brave doesn't preclude someone from being a bully.