Possibly honours a Lawrence; ‘Saint’ was added because a Lawrence Avenue already existed.
According to the Stratton Park local-history website, the street may have been named after Cyrus Jay Lawrence, one of the financial backers of the Park Versailles real-estate venture, or after a Lawrence family in the Town of Westchester. It was to be called Lawrence Avenue, but a street of that name already existed, so ‘Saint’ was added.