The short answer is no - socket manufacturers did not require lamps of a specific manufacturer to be utilized in their sockets. Additionally, I don?t think that Bryant ever made incandescent lamps.
In earlier times before the common Edison lamp base become standard, many incandescent lamp manufacturers did use proprietary bases on their lamps that would physically only fit sockets of corresponding design. Generally, such sockets were not limited to any one specific manufacturer. For example, Bryant produced sockets to accommodate lamps with Edison screw bases, Westinghouse pin bases, Thomson-Houston type bases, etc. until the demand faded for the older obsolete types.