Well, I am going to guess that it takes 1 hour 15 min to get from Lexington to the Ohio border.
That in mind, once you hit OH, stay on I-75 North for 134 miles until you hit a small town...Beaverdam. (approx. 2 hours depending on speed) It is exit 134, and there is no re-entry North-bound. Turn left at the end of the ramp, and go through the small small small town.
Take this road until you can no longer drive it (approx. 14 miles). There are a couple of small jogs, and I think two stop signs. 696 will end, and you will be on road 6...that's right...just road 6.
At the dead end, take a right on to Old St. Rt. 224. Gilboa quarry will be approx 2.5 miles down on the right.
That's it....once you get off of I-75, it is a left off the ramp, a right at the dead end, and a right into the quarry.
Just a forwarning, once you get off 75, you won't see civilzation until you hit the quarry...it is farm country from 75 to gilboa.
Total travel time should be like 4 hours. (if 1:15 is correct from lexington)