Does the lemon law have a specific time limit

Each state has different Lemon Laws but typically this is what most of them say... A car is considered a lemon if it was sold NEW after January 1, 1987, and has a defect or condition that substantially impairs the vehicle (which means the motor vehicle is unreliable or unsafe for normal operation); and the manufacturer, its agent, or authorized dealer cannot repair the vehicle after three attempts (for the same problem) or the vehicle is out of service for repairs for a cumulative total of 30 or more days during the term of protection. Under the statute, the manufacturer must replace the motor vehicle or refund the purchase price (but they can allow for some depreciation).
The term of protection is defined as one year from the date of original delivery or the term of the warranty, whichever comes first. Susu

In some states, a single defect that might cause serious injury makes your car a lemon if the manufacturer cannot fix the problem within 1 attempt. Be sure to keep all of your records, receipts and repair history.

Laws vary state to state, but a rule of thumb is if the car problem can’t be fixed with 4 tries or the car has been out of commission for more than 30 days during the first year or 12,000 miles, your car most likely qualifies as a lemon.

A lawyer familiar with state lemon laws can help you determine a variety of problems like: was there damaged to your car at the time of delivery, deception, fraud, defects that may have been covered up by repairs etc.

Lawyers will investigate the history of your vehicle and submit the details to the manufacturer. At this point, the manufacturer either fixes the problem or ends up in court.

I would check out this website for details on the lemon law statutes for your state http://lemoncarlemonlaw.com/ .