Lock with car Symbol on Security light?

Welcome back to 2CarPros. Is it on solid or flashing? Solid means that after it started the system stopped being able to read the keys transponder. To see which part has the fault you need a high level scan tool that can access the pass-lock system and see which component has failed. The body control module and the anti-theft modules are common issues but you still need the scan tool to test it and program any replacement to the car. Depending on what component has failed the engine may or may not start. You could try a different key or replacing the battery in it but they normally don't cause this issue without giving a warning that the battery is low.

THis guide can help reset the system

https://www.2carpros.com/articles/how-to-reset-a-security-system

Please run down this guide and report back.

Who did the scan? Unless it was a dealer level tool it usually won't be able to read the codes that the anti-theft sets. With it being an intermittent problem I would suspect the ignition switch as that is the moving part but it would need to be tested to see if it's the switch itself or the wiring. When did the light come on? When you turned the key to start or after the engine started and you released the key back to run?

That's what I suspected, their free scan tool only looks at the engine and transmission codes that the OBD system has to display. There are a lot of codes their system cannot see.
After starting suggests it is losing contact with the key. A better scan tool should be able to read the security system. Plus on the higher level tools you can watch what the system sees as it operates. Unfortunately a good scan tool isn't a cheap item.

Dealer, or a good independent shop who is up to date on vehicles. Depends on who you have in the area and who you trust.

Well that isn't a code related to the security system. P0049 is an engine code that indicates the supercharger is running overspeed, except it isn't a code your vehicle should show as that isn't a monitored item.
A P0449 is a valid code for your G6 but it is an EVAP code and should not light the lock symbol but the check engine light only.
Who did you have scan it?

Well they should have used a capable scan tool. Looking in the GM codes list for your vehicle P0049 isn't listed as a valid code though. I would also expect the code that is setting that light to be either a B or U prefix. The attached is the test used if the light is on all the time. In your case it is intermittent but could be related.
This requires a bi-directional scan tool to test the system.