No it cannot, sorry. The 3DS cartridges have an extra tab on the side of them so they don't fit into the DS Lite slot. The 3DS software is also incompatible with the DS Lite, so even if the cartridges did fit, you would not be able to play the game.
So unfortunately, if you do not already own a console in the 3DS family, you're going to have to buy one to play X and Y and future Pokemon games.