I managed to pick up the Collector's Edition strategy guide, and with a little digging, I figured out what exactly was going on. Alot of things could go multiple ways- the stupid strategy guide even says something along the lines of, "Weeeell, it could mean this OOOOOR, it could mean this! Hahahahaaa, we won't give you a straight answer so wait for the next gaaaame." That kind of crap.
ANYWAYS!
They probably throw Desmond back into the animus to wake him up from his shock of possibly killing Lucy. It doesn't address this directly, but I'm sure that's what it's come to. ALSO, they won't be done with Ezio JUST yet- remember at the beginning when Desmond saw the ghost of Ezio in Altair's Armor Chamber? Ezio was really old. Desmond even comments on the fact that he had gone back there for some unknown reason- they never mentioned it again afterward.
There's also that Templar/Enemy trail outside in Present-day, leading to the mansion. Though if you use Eagle Vision inside, everyone is an ally. You'd think Lucy is a Templar, but this game wouldn't be as interesting as it is if it were predictable now, would it?
At the end, the reason he kills Lucy is because there is a plan that has been formulated by the First Civilization. It is a very complex and detailed plan- ESPECIALLY considering that that woman's projection you continue to see is only a projection. Their race died out a LOOONG time ago, remember? Everything she said isn't real-time. She's already Dead. This indicates how much power their race had- to look thousands of years into the future to plan this entire sequence of events to save the world. Anyways- this plan is that the SON, not the SUN, is supposed to be the key to civilization, or something along those lines. Subject 16 reveals the two characters- "Adam" and "Eve". Its also revealed that the reason why Desmond is able to actually ACTIVATE the Apple of Eden is because he is a direct descendant of Adam- the same way that only Ezio was able to actually USE the PoE, as well. 16 also says that Adam must be united with Eve to have a SON. But it's obvious that Desmond is quite fond of Lucy. Lucy, in the eyes of the First Civilization Woman, is a distraction to Desmond and therefore cannot be allowed to live. Also, she refers to Lucy as a "Sharpened Cross", which could mean one or both of these things- 1)Desmond cannot "Cross" breed with the wrong person. He is supposed to be with Eve. 2) Lucy is still a Templar, set to try and earn Desmond's trust and knowledge. This would explain the trail of red on the ground outside. If it turns out to be both of these, the Woman could be hinting a calamity being produced from the blood of an Assassin and the blood of a Templar being mixed. Like I said- it could go both ways. Perhaps Lucy IS a Templar, but because she has grown so fond of Desmond she has changed her mind? Perhaps the red trail is her leaving to deliver information to Abstergo? I guess we'll find out in the next game.
Regardless- after reading everyone's posts, I like the Shroud idea

That sounds really plausable~
Also, there has been a rumor--- RUUUUUMOOOOR, NOT CONFIRMED, MIND YOU, that the next game could possibly be set in the time of the Mayans. The beginning of OUR civilization and such, and Cortes is bringing religion over, as well as the basis of government. There was also all of that hooplah about there being alien markings on the temples and such.. sort of like the Egyptians. I think that the next game will go MUCH more into depth about the First Civilization, for SURE. They've gone 2 games without explaining it much, so it's high-time they start. xD
Should still have ALOT of present-day play though.
Anyone else ever see the Scene when Desmond says "Eeey, Whassamatta you Altair?" To the statue? Everyone I know missed that scene, and it was the best moment of my life xD