The best case for the father of her first [Porter] child has been made. (Comments are welcome!)
Mostly by word of mouth, I had learned that her second child was almost certainly by a different father, of the surname Tew.
This indexed matched record has come up on Ancestry for the profile that I have for Lucy Fann which had an attached profile with only the surname Tew (I have since fleshed it out more, but it may be a blind alley, as no additional index matches have emerged). If someone with Ancestry access can get the details on the birth year of the partner, it may be ruled in or out as a possible match:
Andrew J Tew, who was living in [Township?] Clinton, Sampson County in 1860 Ancestry Record 7667 #41479064
She has a nephew who was named Andrew Tew - it cannot be him, as he was born after Lucy's second child was born (and that would be prohibitively close, anyway). It is entirely possible another line of Tews were also living in the region, but I haven't had any luck searching FamilySearch.