Nice score on inheriting a very nice box! I was lucky enough to inherit one from my grandfather as well.

I was also fortunate enough to get the original keys to my box and might be able to point you in the right direction. If you have the same original lock, the lock is made by Illinois Lock Co, which I found still exists! I did some searching and was even able to find a matching key blank. I would buy some of the Illinois Lock Co key blanks and take them, along with the lock to a locksmith and he should be able to cut them to fit it. In my case I had the original keys and made a bunch of extra keys to carry on my daily carry key ring, spares in case a few were cut improperly, and some more to prevent against loss, so now I have like 8 keys for my toolbox! I keep the originals separate with my Model A keys. I pretty much could only find the key blanks in a single eBay auction although a locksmith might have more access to finding such things. I just bought the blanks and had them cut to my existing keys, however in your case you could bring the blanks and the lock to a smith and he might be able to work something out.
They key blank is Illinois 1041P.
Here are a few photos of my toolmobile.