I am a traveling Elk and we stay at Lodges whenever we can. The Elk International web site will provide lodge location and may indicate the availability of overnight parking - not all lodges have space or are permitted to use their space for overnight parking by local ordinance.
AS members of FMCA we joined the FMCA Elks Chapter (not a lodge) which maintains a web site with camping information for members. In practice I always call a lodge I intend to stay at as far in advance as I can to learn if they do indeed have space and whether they may have an event scheduled that would prevent our stay. Even if they don't charge for parking I will leave $10 donation for the priviledge.