Carrie Fisher's daughter was on the move moments before her famous grandmother, Debbie Reynolds, suffered a possible stroke.

Billie Lourd ´╗┐hauled some luggage Wednesday in Santa Monica with rumored BF Taylor Lautner ... lending her a helping hand and a shoulder to cry on.

TMZ broke the story ... Debbie was rushed to a hospital shortly after 1 PM after someone at the Beverly Hills home of her son, Todd, called 911. Debbie was taken to the hospital in fair to serious condition.