Canon doesn't give a direct answer to your question, so I'm going to try and give you a good subjective answer based on canon.
A: No, Lily's enchantment did not extend past the events in the Forbidden Forest.
A Brief Recap
It's important to remember that Lily's sacrificial charm was between her and Harry, until Voldemort took Harry's blood in Goblet of Fire for his resurrection potion. As we know, this bound Voldemort to Lily's enchantment and created the reciprocal bond between Harry and Voldemort. In Order of the Phoenix, Dumbledore confirmed that the only way for either Harry or Voldemort to survive was for one to kill the other. In Half-Blood Prince, we learn that, specifically, Harry would have to die in order for the scrap of Voldemort's soul that had latched onto Harry to die and allow Voldemort to finally be killed.
The Forbidden Forest
In chapter thirty-four of Deathly Hallows, The Forest Again, Harry allows Voldemort to (ostensibly) kill him; Harry enters a state of limbo (Call this state whatever you like; I just happen to use "limbo".). The way I interpret canon suggests that it is at this crucial moment that Lily's charm has to have changed in some way (Or at the moment Voldemort cast Avada Kedavra on Harry in the forest.). Now, the "neither can live while the other survives" portion of Professor Trelawney's prediction is ... I don't want to say it's been rendered moot, but a very important change has occurred, which touches on the prophecy: Whereas he couldn't before, because of his Horcruxes, Voldemort has now, unknowingly, moved into a position where he could possibly be killed.
King's Cross
What struck me about the King's Cross chapter in Deathly Hallows is that Harry is able to choose whether to die or to live. Since Lily's enchantment would not let Harry be killed by Voldemort, the fact that Harry has the option to die indicates to me that Lily's enchantment has been, if not lifted, at the very least changed. Otherwise, Harry's only option would have been to return to life. But he had a choice between life and death (Again, call "on" whatever you like. I think it means death.).
‘I’ve got to go back, haven’t I?’
‘That is up to you.’
‘I’ve got a choice?’
‘Oh yes.’ Dumbledore smiled at him. ‘We are in King’s Cross, you say? I think that if you decided not to go back, you would be able to ... let’s say ... board a train.’
‘And where would it take me?’
‘On,’ said Dumbledore simply.
Deathly Hallows - Page 578 - Chapter thirty-five, Deathly Hallows - Bloomsbury
The Battle of Hogwarts
Adding on to CCHP's answer, I want to go a little further into the quote CCHP provides, because I think it's immensely important. So, Harry and Voldemort are duelling:
‘You won’t be killing anyone else tonight,’ said Harry as they circled, and stared into each other’s eyes, green into red. ‘You won’t be able to kill any of them, ever again. Don’t you get it? I was ready to die to stop you hurting these people –’
‘But you did not!’
‘– I meant to, and that’s what did it. I’ve done what my mother did. They’re protected from you. Haven’t you noticed how none of the spells you put on them are binding? You can’t torture them. You can’t touch them. You don’t learn from your mistakes, Riddle, do you?’
Deathly Hallows - Chapter thirty-six, The Flaw in the Plan - Page 561 - Bloomsbury
Harry, through his willingness to die to save the others in the wizarding world, created a new enchantment, the same kind of enchantment that was created when Lily died to save Harry. It's unclear to me whether the new enchantment was specific to Voldemort, or whether it was more general enchantment and just kept others safe from dangerous spells, no matter who casts them. Perhaps this is better asked as a separate question. It's clear, though, that Harry and Voldemort were not acting under Lily's enchantment as they duelled in the Great Hall -- they were acting under Harry's new enchantment. There's one more bit of info that suggests Lily's enchantment did not extend past the King's Cross chapter in Deathly Hallows.
The Epilogue / Harry's Scar
The last trace of steam evaporated in the autumn air. The train rounded a corner. Harry’s hand was still raised in farewell.
‘He’ll be all right,’ murmured Ginny.
As Harry looked at her, he lowered his hand absent-mindedly and touched the lightning scar on his forehead.
‘I know he will.’
The scar had not pained Harry for nineteen years. All was well.
Deathly Hallows - Epilogue - Page 607 - Bloomsbury
Harry's scar tethered him to Voldemort; this connection occurred when Lily's enchantment was created.
J.K. Rowling: Well, of course the pain he feels [in his scar] whenever Voldemort's particularly active is this piece of soul seeking to rejoin the master soul. When his scar is hurting him so much, that's not scar tissue hurting him. That's this piece of soul really wanting to get back out the way it entered. It really wants to- it entered this boy's body through a wound, and it wants to rejoin the master. So when Voldemort's near him, when he's particularly active, this connection, it was always there. That's what I always imagined this pain was. Yes, so there you go.
J.K. Rowling - Interview with The Leaky Cauldron - 12.30.07
I was unable to find any example of Harry's scar hurting past the King's Cross chapter (But please do correct me if I'm wrong.). I submit that Lily's enchantment is broken at this point -- Harry does not need her protection anymore. As noted above, he has conjured his own protective charm that protects the Hogwarts students and the Order, and, presumably, himself. That Harry's scar ceases to hurt shows that his connection to Voldemort has been broken. Accordingly, Harry's desire to protect others with a new love-based enchantment shows he may have shed Lily's enchantment in an act of altruism to save those who he loved, and who were alive, rather dwelling on enchantments, however loving, of the dead. I think this, or something like this, happened when Harry was at King's Cross in Deathly Hallows.
