Lavros’s name day is August 18, the feast of Floros and Lavros.
Churches that follow the Old (Julian) Calendar keep the same feast on August 31 of the civil calendar. See everything commemorated on August 18.
The saint behind the name

Floros and Lavros
August 18, Martyr, Φλώρος και Λαύρος
Sts. Floros and Lavros were brothers, stonemasons by trade, who labored in Illyricum in the early centuries of the Church. Hired to build a pagan temple, they gave their wages to the poor, and when the work was done they gathered the poor together, overturned the idols, and consecrated the building to Christ. For this they were put to death, according to tradition cast into a well.
Also celebrating on August 18
These names share the feast, many of them other forms of the same name:
What to say on a name day
The Greek wish is Χρόνια Πολλά (Chronia Polla), “many years.” A call or a short message on the day is what people remember. See name day wishes you can send and what a name day is.