21counter; welcome to TFL!
The way I transport is locked container for each gun (whether rifle, shotgun, or handgun) with the ammo in a range bag; not having any locked handgun cases within the rangebag. I drive a truck, and I'm not putting $$$$ worth of guns in the bed; nor $$$ worth of accessories and range items either. The back seat is where it all goes.
If anyone knows for a fact that there is something there that I could get "busted" for, let me know. Better safe than sorry. But I don't think a LEO will right you up for that unless you were doing something else bad (drugs in car, really bad speeding or reckless driving, etc. ). Most LEO are very rational, nice people.
When you bought your handgun, they probably assumed the lock that the PD gave you was "Fresh". The law requires that you have proof of purchase no older than 30 days. Most of gunlocks are still in new in container, somewhere in my closet, but have been there for months. I buy most of my guns from a dealer than gives you a free lock (via project child safe) with each gun. But, this is thru a small dealer who makes AR's into CA legal rifles (sealed mag well, it still gets all the "evil" features of its "brothers").
But I figure "Oh Well", the $10 lock is worth 1/200 of the rifle, so why worry? If you can afford a gun, you can afford a lock; even though you shouldn't have to buy one.