Why not try the ship itself ?
The first Lancaster was not a UK built warship.
She was passed to Britain, by the US, under the 1940 Lend/Lease agreement, and therefore she would probably have not been given a Motto, alternatively the current Lancaster may have adopted the home town's, have you tried them ?
edited to add: This was the first '
modern' warship - the first one was wooden, built in the late 1600s. So it is possible that the curent destroyer may carry the motto of the city of Lancaster ?