Lemuel Luverne Cady was born to Corneptin Place and Lemuel Cady.

In 1850 the family is in Sheffield Twp, Warren, Pennsylvania, three counties west of Tioga:

Cady, Lemuel 30, Penn
Cady, Camehtion 26, Penn
Cady, Lemuel 8, Penn
Cady, Ellen 4, Penn
Cady, Latmer 2, Penn (female)

Lodina came in later:

In 1860 the family is in Farmington Twp, Tioga, Pennsylvania:

Lemuel Cady, 44, Penn, farmer
Lodina Cady, 35, NY
Loren Cady, 16, Penn
Jerome Cady, 7, Penn
Lemuel Cady, 74, Conn

"Loren" is probably Lemuel Luverne. It looks to me like the gap between "Loren" and Jerome is where Corneptin died. I can't find a death record for her. I'm assuming Ellen and "Latmer" died too. Finally, I'm assuming Jerome is the son of Lodina and not of Corneptin.