I just spotted this notice on the website of Mike Mauder, co-author of the excellent walking guide "On Foot - Circular Walks on Lesvos"
<<<<Walk 5: A City Walk through Mitilini
Page 26, paras 2 - 3, points 20 to 21: The coast road between the lighthouse and the lower castle gate is closed to traffic due to a large-scale archaeological dig, which is scheduled to continue until the end of 2014. We have been assured that it will continue to be possible to cross the site on foot throughout the work>>>>
We often use this road as an alternative to negotiating the busy city centre streets. It was built as a relief road in the 1960s, when a section of the castle, including an Ottoman gate, was partially demolished to make way for this attractive alternative route to Novembriou street, with the sea on one side and the green pine-clad slopes up to the impressive castle walls on the other.
There has been on-going restoration of the Kato (Lower) Kastro complex, with its ruined mansions and a bath house in this area so assume they have now found something of further potential importance.