Hey there Carol,
Welcome to planDisney and thank you for your question! While I haven't personally had a chance to take a grand circle tour around Disneyland Park in the
Disneyland Railroad's presidential car, the Lilly Belle, it sounds like a magical experience!
From what I've been able to dig up, it sounds like the best way to hitch a ride in this car is to keep an eye out for special events and tours, like the
Disneyland Railroad Guided Tour, which have been offered at various times throughout the year.
In my experience, these
guided tours are really a hidden gem at the Disneyland Resort. They are very reasonably priced and the best way to unlock extra magical opportunities that the general public typically don't get to see or experience. A few years ago, I got to visit Walt's Apartment above the fire station in Main Street, U.S.A. It was incredible!
Additionally, you could always ask a Cast Member at the Disneyland Railroad to see if the Lilly Belle is available - you never know!
Thanks again for your question, Carol! I hope you have a wonderful time on your next trip to the Happiest Place on Earth.
Have a Magical Day,
Greg