Born to in the quartiere of Santa Croce, Florence, to a family of limited means, his education led towards an ecclesiastical career, studying at the Collegio Eugeniano affiliated with the cathedral for nine years.
After becoming a priest, he attended the seminary of the diocese, where he met the fellow scholar Giovanni Maria Lampredi, future professor at the University of Pisa for canon law and public rights.
With the arrival of the progressive Habsburg-Lorraine Grand-Dukes, Lastri joined a large academic, multivolume effort, under their patronage, to eulogize famous Tuscans.
In 1776, he published a six-volume set of observations on cultural monuments and buildings in Florence, which proved as a guide for the sophisticated foreign travelers.
The work, titled L'Osservatore fiorentino sugli edifizj della sua patria, with the help of Giuseppe del Rosso, continued to be published for some decades.