Please feel free to introduce yourself in the "new members" forum. :wayhappy:
As to your question - it's not a separate key. You may have to push the key in a bit to allow it to lock or, as sometimes happens on these bikes, the lock may have been damaged in the past. Usually when that happens, it is stuck in the lock position and the lock might be disabled because of the "fix" to get it unstuck.
As stated above, it may have been damaged by a prior owner. But try turning the handlebars all the way to the left, insert key, push and turn the key to the left. If that doesn't work, the only way to find out if it has been damaged is to remove the ignition switch, and you would need to buy a set of Security torx bits for that.
I didn't get a key for the steering lock on my VL1500 when I got it, plus it is easy to break to begin with, so I just use a caliper lock also. I bought mine at my local Suzuki dealer. Around 25 bucks I think.