If you're looking for a meeting place or a good stop around ½ or halfway between Lindsay, CA and Delano, you can try Terra Bella, CA, which is about half an hour south of Lindsay, CA, or about half an hour northeast of Delano.
About ⅓ or a third of the way, you can stop at Hope, CA. This is about 17 minutes south of Lindsay, CA.
About ⅔ or two thirds of the way, you can stop at Vestal, CA. This is about half an hour south of Lindsay, CA, or about 17 minutes northeast of Delano.
About ¾ or three fourths of the way, you can stop at Richgrove, CA. This is about half an hour south of Lindsay, CA, or about 12 minutes east of Delano.
If you drive straight through without stopping at all, the total distance is 39 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 49 minutes.