I only own Lucie. Everyone else belongs to his or her rightful owners. Sorry if Snake is OOC, but I'm not sure how he acts considering he only says so much…
For his entire time in the circus, he was being lied to about their real motives. When he found out from Sebastian and Ciel, he felt betrayed by the people he called family.
Working in the Phantomhive manor was all right, but Ciel was lying to people who called him a friend. Snake felt their betrayal for them.
So, when Snake met Lucie, he was nervous. He wanted to get closer to her, but didn't want to be betrayed again. The scars were already deep enough. Lucie wants to get to know him, but he keeps her at a distance.
When he finally let her in, he found out that her "family" also betrayed her. However, hers was on a much greater scale. This betrayal left bleeding wounds on her heart and soul. After Snake found out, he decided to be someone she's never had before.
"'Lucie, I promise to never hurt or betray you. I promise to be an honest friend,' says Woodsworth."
And he promises to keep every word until the day he dies.