Family Search shows the following:
This is a birth record for Elias Lothrop in Leeds, Maine, born 7 July 1853. Parents are listed as Davis Francis Lothrop and Caroline S. Morse. Father was 33, mother was 28.https://familysearch.org/pal:/MM9.1.1/2HKT-S46
This one shows the birthplace was actually Androscoggin, Leeds Co.https://familysearch.org/pal:/MM9.1.1/F4SV-7VF
1870 census - Elias L. Lanthrop born 1853-1854 in Maine. Head of household is Dennis F. Lanthrop and Caroline, presumably his wife. Location – Androscoggin, Leeds Co. Looking at the image, I can see where the father could be DAVIS F. Father is 49, mother is 46. Census was taken July 1st. There is an Irvin in this household, aged 14.https://familysearch.org/pal:/MM9.1.1/M6DC-4N1
This 1870 census shows an Elias L. Lanthrop, 16, in the home of a Jane Lanthrop, 49, in Cumberland, Brunswick Co., Maine. Note there’s a Cassie Keay, 23, in the household. There’s also an elderly woman named Jane Morse, 79, living in the home. Census was taken June 13th.https://familysearch.org/pal:/MM9.1.1/M6D8-B2C
I believe these two Elias L. Lanthrops are one in the same, and that he was visiting his Aunt Jane Lanthrop in June and was back home in July.
1880 census Plaquemines Parish – Elias L. Lanthrop, 25, born in Maine, living in the home of Silas Sawyer & wife Carrie K. Sawyer, 34. Elias is a cousin to presumably Carrie/Cassie. Also listed in the household are Aunt Jane Lanthrop, 58, and cousin Irvine Lanthrop, 22.
This appears to be the same Elias L. Lanthrop living in Plaquemines Parish in the 1910 census.https://familysearch.org/pal:/MM9.1.1/MPY5-LFZ
I would say this is a pretty strong case toward proving that these Lanthrops are the same family found in the history of Leeds County.
In the above mentioned 1910 census, Elias’ daughter Jane Lanthrop Houston is living with them. Here’s a death record for Jane showing her mother’s maiden name as Lucille Pioget. Jane was married to Samuel Houston. It also shows that Elias' wife, Lucille, stated that her father was born in Switzerland.https://familysearch.org/pal:/MM9.1.1/FSBQ-88W