If you're looking for a meeting place or a good stop around ½ or halfway between Orlando and Lake Placid, you can try Lake Wales, FL, which is almost an hour south of Orlando, or about 1 hour north of Lake Placid.
Another possible place to stop near the midpoint is Cypress Gardens.
About ¼ or a fourth of the way, you can stop at ChampionsGate, FL. This is about half an hour southwest of Orlando.
About ⅓ or a third of the way, you can stop at Haines City, FL. This is about half an hour southwest of Orlando.
About ⅔ or two thirds of the way, you can stop at Avon Park, FL. This is about 1½ hours south of Orlando, or about half an hour northwest of Lake Placid.
About ¾ or three fourths of the way, you can stop at Sebring, FL. This is about 1½ hours south of Orlando, or about half an hour north of Lake Placid.
If you drive straight through without stopping at all, the total distance is 101 miles. The distances shown above don't include local roads to get into each town, so if you're planning a long road trip, make sure you factor in traffic and road conditions, rest stop breaks, and interesting detours along the way. If you're in a rush, you can do the trip with zero stops, and your total travel time would be around 2 hours, 2 minutes.