Buying and Selling in California?

I think it has to be within 3 months. When you take the transfer of title form in to the dmv they will give you two months to get it to pass smog.

Smog certifications are good for 90 days from the date of the inspection so you will need to get it smogged. I don't know what year Lexus your buying but when you transfer a vehicle that is four or less model years old a smog certification will not be required. If the Lexus is more than four model years old, evidence of a current smog certification must be provided by a seller except when the transfer occurs between a spouse, sibling, child, parent, grandparent, or grandchild.
Oh also just so you know if you purchase or acquire a vehicle from a private party, you have 10 days from the date of sale to report to DMV the change of ownership. Transfer fees must be paid to DMV within 30 days of the purchase date, even if you do not have all of the required documents. Failure to pay your fees to DMV within 30 days will result in transfer and use tax penalties.