In the world of Dracula, if you don't want to have your blood sucked, you better down a lot of Red Bull, because being asleep tends to get you bitten. When Jonathan Harker is staying at Castle Dracula, the Count warns Jonathan not to fall asleep in any room but his bedroom. When Jonathan falls asleep in another room of the castle, he almost gets bitten by the Brides of Dracula. Lucy is an easy target because she sleepwalks: once she's asleep, Dracula can influence her more easily and make her walk out of the house, where he can suck her blood.
Why are half-asleep people more easy targets? Well, obviously, sleeping people are less able to defend themselves physically. But their guard is down in other ways, as well. The novel suggests that almost everyone (even Mina and Van Helsing) have some kind of secret, deep-rooted desire to be bitten – they just keep it repressed most of the time. But when they are half asleep, or sleepwalking, the desire bubbles to the surface. When asleep, their conscious minds aren't able to keep that naughty desire under wraps.