Would it be possible that you mean “Litespeed” and not “Lightspeed”? If yes the product description of this propriatary software says:
LiteSpeed Web Server (LSWS), is a proprietary web server software. … The software uses the same configuration format as Apache HTTP Server and is compatible with most Apache features.
Due to this I would recommend to search the administrator guide and/or the forum for information how to configure “.well-known” redirects.