Hi! We are currently researching your Lucy's grandmother and grandfather, she was also named Lucy Carter Hinckley (1st), and was married to William Hinckley who (we think- but can't confirm) is our maternal connection.
Your Lucy's father was Hiram B. Hinckley (Lucy 1st and William Hinckley's child) married to Maria Wooding and they had quite a few children: Lucy-1859, Sabra-1860, Frederick-1863, Carrie-1865, Charles-1867, Minnie-1869, William-1876, Florence-1874, Blanche-1873.
My current research does not show Lucy (2nd) as being married or having any children, but that could just be an error on my part.
Hope this helps you. If you have any information on William and Lucy where they were born, children etc..we would GREATLY appreciate it! If I can be of any further service don't hesitate to contact me!