Lucina's brother, Joel Almon Bascom is also in the 1856 Philemon C. Merrill pioneer company, and a Lucina A. Burton's name is listed on the company roster in the Deseret News immediately after Joel's. We do not see any connection of her to the surname of "Burton," so we are not sure if this refers to our Lucina. She married Joel Hills Johnson in Hancock, Illinois, so she would have come to Utah with the surname of "Johnson."
The obituary of her son, Joel Andrew Johnson, states that he came to Utah with his mother in the 1856 Philemon C. Merrill pioneer company. (See: https://www.familysearch.org/tree/person/memories/KWV5-K5M )
Note that FamilySearch shows her given name as "Lucinda."
Her birth and death dates are confirmed by the inscription on her gravestone, which shows her name as "Lucina H. Johnson."
The 1860 Utah census shows her name as "Lurina C. Johnson."