Lucy is utterly incapable of displaying affection and would bite off his remaining hand to avoid doing so publicly. It's always some roundabout gesture with maximum deniablity with him in case the feeling isn't mutual. Gotta keep his heart safe, it's his only weakness.
If Lucy is genuinely interested in somebody he gets very unsure of himself and tends to play it slow and safe, he's had plenty of weekend flings and one night stands with no attachment but if he really wants to woo them? He'll take it slow and be attentive, learn about them, share in their interests, listen to their stories and experiences and take note of their preferences like food, clothes, music, poetry, art and more.