My security light is on and off, and some times my chevy lumina won't start.

Check fuses
I found fuse box diagram which one of the fuses is for Theft-Deterrent Module, Radio. I would go through and check fuses
Chevrolet Lumina (1997) - fuse box diagram - Auto Genius
Some info no theft-deterrent below
1997 Chevy Lumina Car Will Not Start. "security" (2carpros.com)
Security System Preventing Car From Running: Car Will Not Start, ... (2carpros.com)

check your battery first, then check your ignition switch, then check your spark plugs and wires.

There may be a problem with your antitheft security system. This will turn off the starter and make it appear to not be functioning properly. Look for a light that says SECURITY when you try to start your car. If you see that light, go to this link for help.

http://vatspasslockpasskeysecurityhelp.yolasite.com/

Here is a link that will help you understand the problem. There are also some ways to beat this yourself.

http://vatspasslockpasskeysecurityhelp.yolasite.com/

security light off, have someone hold the key to start and tap on the starter and see if it spins
if it does you need to replace the starter.

Check the dash once you turn the key to the run position the passlock runs a security check using a set resistance value through the chip in the key. If the security light begins to flash the reading it received was incorrect or it didn't get a reading at all. You can try reseting the value it is looking for by turning the key to start then releasing it. After 10 minutes turn it off then cycle it start again leaving it in on for 10 minutes then back to off then one more time. After the third cycle has completed for a total of 30 minutes. You should be able to turn the key on and start the vehicle. If the light continues to flash their is a problem with the chip in the key or the connections within the ignition its self. Both are common but a Pass Lock Relearn as described above will usually adapt to the poor connection values. Hope this helps.

Sounds to me like you are right. Read up on this link. You'll find an answer to you problem there.
http://vatspasslockpasskeysecurityhelp.yolasite.com/

Are there any lights on the dash when this happens? When you put key in and try to crank it over, does the securty light come on?

FUSES ON THE LEFT BELOW OVERFLOW JUG AND FUSES TO THE RIGHT FENDER WELL NEXT TO WINDSHIELD WASHER FLUID RESERVOIR.YOU ALSO HAVE FUSES INSIDE VECHICLE ON PASSENGER COMPARTMENT ON THE RIGHT INSTRUMENT PANEL.

check your inteior light switch. for a tempory fix remove the bulb