Would using a drysuit in water this warm be too warm?
No.
I'd rather not sweat in my suit. However I'd also rather not rent a 3 or 5 mm wetsuit for an entire semester.
You won't necessarily sweat in your suit under water. The bigger question is what are the ambent air temperatures, and how long will you be in a zipped suit on the surface, in the sun, in warm air, before (or after) going in the water.
The water ranges from 20-28C, or 68-82F from what I am told.
You should be quite comfortable in a drysuit at 68F. Your body temperatiure is still substantially higher than the ambient water temperatiure. So, you still lose heat (in a wetsuit) even if the water temperatire is in the low 80s.
You will probably notice the difference in temperature on ascent, presuming the water is colder at depth, and warmer toward the surface, and it could feel quite warm for a few minutes.
Could I get away with wearing a lycra suit (to prevent chafing) and the drysuit?
Yes. In diving a trilam suit, you can easily vary the thickness of the undergarments. There is nothing wrong with wearing a simple lycra suit under the trilam drysuit, although you might actually be a little cold in 68F water.
As a comparison experience, I have dove the Oriskany a number of times in summer - usually around July 4th. I always wear a drysuit, even though the air temperatures are in the mid/upper 90s, and the humidity is very high. But, I also know I am going to be in the water for 80-90 minutes. The water temperatires at the bottom are in the mid-60s, and I am very comfortable. Where I feel 'warm' is coming up through the thermocline into the low 80s water, and usually the beginning of my last deco stop, at 20 ft., is a bit uncomfortable. Simply taking my hood off makes a big difference though.
You shouldn't have a problem with a drysuit in the conditions you describe.