Not sure if anyone else has seen this. Basically if I look at flights from FRA to NYC in the next few days, it shows there's first class availability on Lufthansa direct flight, however if you look closely it shows that the booking class is I (which is business award if I'm not mistaken). Does this mean Aegean is charging first class award price but giving you only a business class seat?

Well - according to LH, the plane on this flight doesn't have first class, so you cannot book it.
Seems indeed to be a mistake.

The same thing has been noticed in the past on a regular basis with tickets for TAP, Air India and Ethiopian (especially the first two were always showing availability in first on Aegean's award search, I think someone mentioned one or two cases with Turkish as well at some point).
Anyway the Lufthansa error is present ever since the award system came back to life about 2 months ago and it has shown "first" for flights on the 747-400 as well as the A350 (which is what this flight is on) ever since. Besides the "I" fare, which does mean business class and doesn't change when switching options from business to first, the other obvious error is the "first" ticket costing "only" 75k miles, when there's a first leg on a short-haul jet, which obviously doesn't offer first class. I live for the day, when Aegean's booking system gets a bug or a loop hole (or even better a complete policy change!), that will enable booking of a mixed cabin at the (very fair) price of the more expensive cabin of the two (instead of the sum of their individual cost, which is what they actually charge).

Since it used to work exactly like that, and they changed it to the current method, I doubt that they will change it back any time soon.