There are several synonyms for "lie close" that can be used to describe a proximity or closeness. One of the most common synonyms is "nestle," which suggests a cozy and intimate relationship. "Snuggle" is another synonym that connotes affection and comfort, while "huddle" suggests a tight formation for warmth or security. "Cuddle" is a similar word that implies affection and closeness. "Cling" suggests a stronger and more dependent attachment, while "hug" is a physical act that implies closeness and warmth. "Embrace" is another synonym that suggests an intimate and loving relationship. In all, there are many words available to describe a state of closeness between two objects or persons.