Lake is approximately half-way between the northern and southern
extremities of the Isle of Wight, and faces almost due east across the
sea. That makes it on the east coast.
I don't propose to argue the matter further as long experience shows
that any discussion with you is pointless.
You have admitted that your claim to be on the south coast was wrong,
which is a small but important step in the right direction for you.
Keep up the good work, and watch out for the trains.