You can search through the online IMEI registries. Sometimes they indicate who locked the device. Most times they do not, or they're inaccurate. But you might get lucky.
When a carrier locks a device it's because it's subsidized - meaning that they can save money and make money by mucking around with the OEM software or installing their own. Apple imposes a lot of restrictions but carriers still get away with as much as they can.
So chances are good that if you do a factory reset on the device you'll find add-on bloatware apps, browser homepage, favorites, etc which are set to the carrier's preferences - and which reveal the "OEM" (carrier) by connecting directly to their "value added" sites and services.
There apparently is (or was) some kind of iTunes plugin which could let consumers check through all the boring system logs and stuff stored on device and click up juicy hidden technical details (like CK lock identifers) ... some sort of dev tool which worked on non-hacked non-rooted non-jailbroken iOS devices but I don't know what it was called or if it's legit because iDon't iTunes and iDon't iPhone.
