How did Dracula get into Lucy's home?

Question

According to Van Helsing, Dracula must be invited before he can enter a home. The zoophague invited him to the asylum. But how could he enter the home of Lucy Westenra?

Answer 1

Assuming you are referring to Stoker's original...

Because Dracula attacks Lucy from outside, through the window

In Lucy Westerna's entries she makes repeated reference to the "noises" or "flapping" outside her window:

Somehow, I do not dread being alone tonight, and I can go to sleep without fear. I shall not mind any flapping outside the window. Oh, the terrible struggle that I have had against sleep so often of late, the pain of sleeplessness, or the pain of the fear of sleep, and with such unknown horrors as it has for me!

Remember that Lucy is also a sleepwalker, so the idea that Dracula can lure her to the window to feed is already setup. As Van Helsing continues to try to defend her with garlic, etc., Dracula ups his game ... but still from either the window or outside. Excerpts from her final memo:

I went to the window and looked out, but could see nothing, except a big bat, which had evidently been buffeting its wings against the window. So I went back to bed again, but determined not to go to sleep. Presently the door opened,and mother looked in. Seeing by my moving that I was not asleep, she came in and sat by me. She said to me even more sweetly and softly than her wont...

The window blind blew back with the wind that rushed in, and in the aperture of the broken panes there was the head of a great, gaunt gray wolf.

Mother cried out in a fright, and struggled up into a sitting posture, and clutched wildly at anything that would help her. Amongst other things, she clutched the wreath of flowers that Dr. Van Helsing insisted on my wearing round my neck, and tore it away from me.

The air seems full of specks, floating and circling in the draught from the window, and the lights burn blue and dim. What am I to do? God shield me from harm this night! I shall hide this paper in my breast, where they shall find it when they come to lay me out. My dear mother gone! It is time that I go too. Goodbye, dear Arthur, if I should not survive this night. God keep you, dear, and God help me!

Since Stoker tells the story through first person diaries and letters, it is difficult to be 100% positive what happens during each of Lucy's attacks - but does seem as though Stoker is intentionally making the point that Dracula is using the window and not actually gaining entry.