Lothal is about 80 km southwest of Ahmedabad. The most straightforward approach is by hired car from Ahmedabad, a drive of roughly 90 minutes. Self-driving is easy on good roads.
By public transport, take the train from Ahmedabad towards Bhavnagar and alight at Lothal-Bhurkhi station. Auto-rickshaws wait at the station to cover the final few kilometres to the site. Return transport is infrequent, so agree a pickup time with your driver or ask at the site about the afternoon train schedule before you arrive.
Organised day tours from Ahmedabad are available and take the logistical headache out of the journey — worth considering if you don't have a vehicle.