I really liked the Lily's character and the actor was far above McFadden's skill, no offence to the latter. She had some great lines in a short amount of time that McFadden could not have pulled off. Plus it gave us a chance to see what a person from that era was like, whereas Cochrane is just a generic drunk, Lily is the kind of guerilla-engineer type of character that we see occasionally like Naomi Nagata in The Expanse.
It's not so much an unorthodox opinion as it is a head-cannon thing, but I like to think Lily is the reason that Earth armed up so quickly with a space navy between the events of FC and ENT (multiple Kzin Wars during that time notwithstanding). She'd actually seen a hint of what was out there and wasn't going to trust Earth's protection to the Vulcans once they established a presence on Earth. Also, it doesn't appear like she actually saw any actual Vulcans while she was on the Enterprise and that had to have left certain questions..