This comes up from time to time -- the short answer is that educated people by the time of the Roman republic would certainly know this, but we can't be as sure about people who are not educated. I've written about it before a few times:
to quote from that first one:
Hipparchus of Nicaea (c. ~190-120 BCE) seems to have been the first person to propose using a grid system to find the position of cities (and other places) on a globe, which implies an understanding of longitude. He built on earlier work by Eratosthenes of Cyrene (c. 276-194 BCE), who had mapped the known Earth, including finding its circumference. Hipparchus' method of finding the longitude of places was to use the differences in timing of lunar eclipses at different points on the globe to calculate the difference between local time of those points; the drawback is that there was no accurate-enough method of timekeeping to lead to useful calculations. Edit to clarify: The difference in local time between observed beginning and end of the eclipses would serve, essentially, as a way to understand the longitude between places.