I am pretty sure you can dive in just about any piece of "public" lake that you want. It's purely your decision to dive or not to dive. I won't claim to know all of the rules but here are the one's I always honor:
1) Boat better meet boating regulation requirements.
2) You better fly a dive flag. Period. No excpetions.
You can buy a regulation dive flag and float at any LDS in the state.
Only fly the dive flag when you are actually in the water. Do not display
the flag during surface intervals.
3) Boaters are required to honor the dive flag. They are required by law to remain at least 100 ft. from the flag at all times. They are required to honor the dive flag. Don't assume that they will. Some boaters are diligent and courteous. Some boaters are a$#e$.
4) Conversely, divers are required to stay within 50 ft of the dive flag at all times.
I don't want to encourage bad behavior so I am reluctant to say this; but I will anyway, most divers interpret this rule as "never surface more than 50 ft from the flag", ie. if you are underwater, swim out 200 yards if you want, just be sure to return to the flag before surfacing.
5) By law, you cannot dive within, I think, it's 150 ft. of any boat ramp. This rule prevents divers from "blocking up" a boat ramp and thus denying it's use to other people (boaters).
6) Other than these rules, I just try to be smart and courteous to other people and boaters, ie. don't dive right in the middle of the lake channel; especially if the lake narrows to 170 ft at that point. It's like placing a blockade at that point in the lake. See rule 3. At the least, it creates a nuisance to the boaters. They won't like it and probably won't honor the flag.