Yes, you can attack these new adjacent regions after conquering the seas or lake. The Seafaring rules state that the seas and lake are considered empty regions for you:
As long as your Seafaring race is active, you may conquer
the Seas and the Lake, considering them as 3 empty Regions. You keep
these Regions even once you go into Decline, and continue scoring for
them for as long as you have tokens there. Only Seafaring races may
occupy the Seas and the Lake
Since they are just regions, the rules for subsequent conquests apply:
The active player can repeat this process to conquer as many new
Regions as he wishes during his turn, provided he has enough Race
tokens left to accomplish these successive conquests. Each of the
newly conquered Regions must be adjacent to (i.e. sharing a border
with) a Region already occupied by his active Race tokens, unless
permitted otherwise by his Race and Special Power combo.
Go forth and conquer!