Lemons entered Italy at latest during the 2nd century according to Wikipedia. It then states that they reached Persia and subsequently the Middle East around 700 AD.
I was under the impression that the Silk Road was the only means of goods exchange between Rome and Southeast Asia during that time. If this is the case, how did these goods make it through the middle east unnoticed in order to reach Rome? If this is not the case, were there other ways of transporting goods at the time? It just seems strange that the middle east, being situated between two areas with lemons, being a hub between the two in trade, missed out on these lemons for over half a millennium.
The Roman empire had sea ports on the Red Sea, which allowed them to conduct a vigorous seaborne trade with the Indian subcontinent. This meant Roman merchants could bypass the overland Silk Road. Citrus fruits had been cultivated in India for a very long time, so there was no need to sail all the way to China. It's even likely that some citrus cultivars originated in India.
However, the Persian Gulf region also traded by sea with India, so that raises the question why the lemon reached Italy long before Persia. The reason is probably found in the fact that there are many varieties of citrus fruit and some had been cultivated in the Middle East for centuries before the lemon arrived in Italy. So it might simply have been a matter of taste, the Persians preferred the earlier arrivals over the new-comer. Or perhaps archeology hasn't found clear evidence of earlier cultivation yet (the reason we know beyond a shadow of a doubt that lemons were cultivated in Italy is because of realistic depictions of plants on murals in Pompeii).
The citrus fruits fell out of favor in Europe when the western Empire fell apart, only to make a comeback in parts of the Mediterranean with the Muslim conquests. Arab farmers brought with them many varieties of citrus fruits, including the lemon, and also spread the lemon to Persia ca 700 AD.