Your ancestor, Vernee Lorenzo Halliday, was the son of George Halliday (full biography). George converted to the Church of Latter Day Saints in 1844 and began working as an LDS missionary in 1845. Your ancestor Vernee Lorenzo was born in 1852, so his father was already fully active in the LDS church.

The reason this is relevant is that Lorenzo Snow was an important figure in early LDS history, particularly in the history of the British missions there. Lorenzo Snow first went to Britain as a missionary from 1840-1843, then returned to Europe from 1849-1852, where he primarily did missionary work in Switzerland and Italy but was also active in Britain.

It was very common to name children after good friends. I would research your ancestor's relationship with Lorenzo Snow.

And as Lorenzo Snow's own name shows, "Lorenzo" wasn't necessarily an Italian-only name.