Also nominated for best picture were James Franco's survival tale "127 Hours," Natalie Portman's ballet drama "Black Swan," Ben Stiller's dark romance "Greenberg" and Annette Bening's lesbian family drama "The Kids Are All Right."
The awards will be presented Feb. 26, the day before the Academy Awards.
"Winter's Bone," which won the top prize at last winter's Sundance Film Festival, also earned a best-actress nomination for Lawrence, who stars as an Ozark Mountains teen on a desperate search through the region's criminal underbelly to find her missing father and save her family home.
The film also picked up supporting-acting slots for Hawkes and Dickey, a directing nomination for Debra Granik, a screenplay honor for Granik and co-writer Anne Rosellini, and a cinematography nomination.
"The Kids Are All Right" was second with five nominations, including a best-actress honor for Bening and a supporting-actor slot for Mark Ruffalo. Co-star Julianne Moore missed out on a nomination for the comic drama about lesbian parents whose teenage children make contact with their biological father.
Along with Lawrence, Bening and Portman, best-actress nominations went to Greta Gerwig for "Greenberg," Nicole Kidman for the grief drama "Rabbit Hole" and Michelle Williams for the marital tale "Blue Valentine." The category had six nominees instead of the usual five.
Besides Franco and Stiller, the best-actor nominees were Ronald Bronstein for the fatherhood story "Daddy Longlegs," Aaron Eckhart for "Rabbit Hole" and John C. Reilly for the romantic comedy "Cyrus."
Presented by the cinema group Film Independent, the Spirit Awards honor movies that cost less than $20 million to make. Other criteria include films' originality, provocative subject matter and percentage of funding from independent sources outside the Hollywood studio system.