Hello,
Move from Lahore at 7am, stay on N5, Use Khanewal-Multan-Lodhran (N5) and not E5, not for cars plus car would lose its life. Have food at Multan, u would be there in 5hours like at 1PM. Then move and Stay at Rahim Yar Khan (Hotel Faran), its like 4-5km inside Rahim Yar Khan Bypass i guess if u go through its newly metalled road. Luxurious, big rooms, 2500-3000 rent, Ac works if needed in this weather, Food is Good, Proper Parking, Garden, Security. Next day move again at 7am, U would be at Moro at 1:30PM-2PM. Stay and have Lunch and move again. You would be at Karachi by Maghrib at 6 or 7pm.
7am time is suitable if family is together else u can go as early as 4, but with family u dont need to rush at 4am when 7 am is suitable time.