If we do not know how lots are cast, then we do not know how to do it. So from a practical standpoint, we can say no casting lots to determine the will of God. Case closed, and sticky doctrinal point turned into a non-issue as far as practice is concern..
But then someone who studied this aspect of the ancient world may say..... actually we do know how they were cast, then open up the can of words again.
The Old Testament did not allow divination, soothsaying, etc. I think an example of middle eastern divination might have been reading filaments in a liver to determine some entity's will. Romans interpreted the flight paths of birds. That's later and far away. I remember the word 'auspicious' and how it is related to the word for birds in Latin and their form of divination when I think about that.
The question about lots is a sticky one, I think, because it raises the issue of what exactly constitutes divination? The tarot card throwers are throwing down so many cards. Is that kind of like casting a lot. But the cards are infused with their practices based on.... whatever..... I'm not sure what's on the cards. I think I heard 'death' on some movie. I am guessing the cards have to do with religion/occult type stuff. I would not imagine the set of options are likely to be divinely ordained. What about Christian themed cards that were being used for 'readings' that someone was posting and complaining about? Is the set of option divinely ordained? Did God reveal cards to put in a deck? It's a whole different situation from a lot representing an individual because it has content on it.
I would guess from reading passages that an individual or group had a lot. The lot could indicate which individual or group was responsible or won a prize or was selected, or whatever.
I have wondered if the Urim and Thummin were basically a set of lots that could say 'yes' or 'no' or not response. But Jewish tradition said they glowed. And the responses from inquiring of the LORD in scripture can be extremely complicated. I suppose they could have asked so many questions and gotten responses and it could have been summarized in the text, or maybe complete sentences were communicated somehow. One theory was that the stones in the breastplate lit up to communicate some kind of message.
These are interesting mysteries, but not that practical for application, IMO, unless you confront people really casting lots to determine the will of God, don't feel right about it, and feel like you have to figure this out so you can tell them something about it.