In episode 4, Lord Fallon compared Lucy to Persephone, a Greek goddess. In Greek mythology, Hades was in love with Persephone so he abducted her and made her live in the underworld with him. When her father ordered her release, Hades tricked Persephone into eating pomegranate seeds so she had to spend half the year with him in the underworld as she had tasted food from it. I think this is why he made her eat them as he does say 'Now you're mine' and also 'these seeds seal your fate'.