You should be able to contact the California Department of Motor Vehicles to find out your Driver's License number, when it will expire and when you will need to renew your license by. However before your license expires you will need to get a replacement driver's license if you have lost your California issued license since you are required to carry this document with you when you are operating a vehicle in CA.
California vehicle code 12500 makes it illegal, and a misdemeanor, to drive without a valid license on any highway in California. A person cited for driving without a valid license in CA may be punished by probation, time in county jail, and fines of up to $1000 plus surcharges.
A separate CA vehicle code, section 12951, discusses having your license in your possession. This VC states that a) The licensee shall have the valid driver's license issued to him or her in his or her immediate possession at all times when driving a motor vehicle upon a highway and b) The driver of a motor vehicle shall present his or her license for examination upon demand of a peace officer enforcing the provisions of this code.
So you could be cited for driving without a license in your possession if you are stopped by law enforcement for a different violation, such as speeding, and are unable to produce your driver's license. You can normally get this citation dismissed if you can show the court your valid license but you must bring in very specific documentation.
What CA laws say is that when a temporary, interim, or duplicate driver's license is produced in court, the charge shall not be dismissed unless the court has been furnished proof by the Department of Motor Vehicles that the temporary, interim, or duplicate license was issued prior to the citation, that the driving privilege and license had not been suspended or revoked, and that the person was eligible for the temporary, interim, or duplicate license.
So it could be a real hassle to get the right documentation and get a citation dismissed by the court if you were found driving without your driver's license in your possession due to the fact you lost it and did not go and get a duplicate or replacement license issued by the DMV.
The CA DMV notes that if your driver's license is lost or stolen you should visit your local office to complete an application form for a duplicate license, pay the required fee (as of early 2008 this was $22), give a thumb print and have your picture taken. You will be issued an interim license valid for 60 days and/or a receipt for your ID card until you receive your new photo license and/or photo ID card in the mail. Your local DMV representative can give you more information if you have questions about receiving a duplicate license.