First off, I am not a lawyer. I usually post memes and shitpost @li8625 as my primary contribution here. Soooo with that out of the way:
If you have an articulated communication text/email from an agent of the dealership that comprises a reasonable offer for your lease deal, I think have sufficient grounds to initiate a claim against the dealership for deceptive trade practice in California. If they clearly made a mistake (like said you could lease a car for $0.99 a month or something), I doubt this will help you.
Before you retain counsel, please advise your dealership that in California, you believe their practice violates the Business and Professions code § 17500 with fines that include jail or $2,500. Furthermore, it seems to violate Cal. Veh. Code § 11713 Prohibited Advertising with penalties ranging from $100 to $1000.
Tell them unless they agree to honor the terms that you had previously agreed via email/text (and thus appeared at their showroom), then you are prepared to submit a claim with proof of deception to the following:
The CA DMV against their dealer license:
The CA Attorney General against their unlawful business practice:
AND
The CA Department of Consumer Affairs:
FTC CARS rule is at the federal level and has been blocked so far by NADA and lawmakers in states that tend to show up as red during an election cycle. You can’t expect CARS to do much here.