The 14ft female has been fitted with a satellite tag by the Ocearch project and was followed as she completed her transatlantic crossing.
At the weekend Lydia, who had a tracking device attached to her in Jacksonville, crossed the mid-Atlantic ridge. She has travelled 19,500 miles in total and is now about 3,000 miles from her initial starting point, after turning back towards Ireland.
Lydia’s journey across the Atlantic is the first time scientists have been able to follow a great white undertaking such a migration path.
Expedition leader Chris Fischer has told the BBC he believes she may be pregnant and heading towards birthing grounds in the Mediterranean – although no-one is sure where or how far she will travel.