If you're looking for a meeting place or a good stop around ½ or halfway between Salt Lake City and Lyman, you can try Sharp, UT, which is about 1½ hours south of Salt Lake City, or almost 2 hours north of Lyman.
Other possible places to stop near the midpoint include Levan, Juab, Red Point, and Mills.
About ¼ or a fourth of the way, you can stop at Spanish Fork, UT. This is almost an hour south of Salt Lake City.
About ⅓ or a third of the way, you can stop at Payson, UT. This is almost an hour south of Salt Lake City.
About ¾ or three fourths of the way, you can stop at Aurora, UT. This is a little over 2 hours south of Salt Lake City, or almost an hour northwest of Lyman.
If you drive straight through without stopping at all, the total distance is 200 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 3 hours, 4 minutes.