your message is a little ambiguous as you have not informed whether you want to go in one go or you are ok with a stop over....
if you are planning to go in a single go then i would highly discourage it. travelling in sindh during night time is dangerous. even if u want to take this option you wont be allowed to travell in various sections till the traffic / local police there has amassed enough cars to drive them in a group for next 30-40 kms... other than the security reason the road condition is mostly mediocre to bad so a first timer will find it difficult. .. the last thing is that you have a high chance of taking a wrong turn and end up travelling with no one to guide you for a few dozen kms...
take a break at either Rahim yar khan or at sukkur... If you know people in Engro, daharki or at FFC Sadiqabad/Mirpur mathelo the stay there or lastly arrange for a night stay at Pano Aqil cantt... Amongst these i would recommend stay at daharki, mirpur mathelo or Pano Aqil... these are almost mid way between Lhr-KCI
now coming to the route..
From lahore leave at around 6 max 6:30 am.. this way you will get out of the lahore district before the school time and the traffic mess begins... and the same logic prevails when you cross sahiwal/okara area... whenever i left after 6:30 i always repented my decision...
the road from Lahore to Khanewal (3:40 - 4 hrs journey) is good and there is no option B for this section... but when you reach Khanewal you can either go to Bahawalpur via Multan (3 hrs) or via Jahania (2.45 to 3 hrs) ... when coming from Lahore it is at the Daewoo Khanewal terminal that you can either take the road that goes straight towards Multan or you take the left side road for the trip to Bahawalpur via Jahania... I prefer and would suggest the road via Multan as the road is better...
when you enter the multan city, 2 kms after crossing pak arab factory you need to take the left turn @ chowk kumharan that will take you to Main bus stand and then towards Bahawalpur... the road till BWP is also good. when you reach Bahawalpur you need to take the road that goes to Chowk Bahadur, Rahim yar khan via Zahir pir (2.45 to 3hrs) ... the road is again ok.. from Chowk Bahadur to Daharki the road is again ok (1.30hrs)
Road from Daharki to Kci (Daharki-Rohri-NawabShah-Hyderabad-KCI) is a nightmare... more than 50% is in a bad shape... you need to show patience and need to be calm... this section will take you 9 hrs approx.
Now.. through out the journey try to get petrol from Total or Shell... nothing else...
before leaving check get engine oil, air filter and oil filter replaced, get the plugs checked..
check air pressure, brake oil, Keep 2 water bottles, 1/2 set of dusters/cloth...
buy a steering lock and when parked over night or more than 10 minutes use it on the on the steering wheel and not the boot / seats....
buy sun shades as during route from Ryk to Daharki the sun will be right at your eye level and it is really annoying...
Keep change ... lots of 10 and 20s along with 5 rupee coins... u will save time at toll plazas...
Take some snacks with you... The recommended and safe places to stop are at hotels on sahiwal bypass,Daewoo terminal Khanewal, hotels before and after sutluj bridge near bahawalpur, Daewoo Chowk Bahadur and then there is a full stop. a big one too. get the gas filled... never leave the car unattended, take a pee in turns and keep ur jokes to urself or in between the colleagues... once you cross SAdiqabad the medium of conversation is mainly sindhi.. people will understand what u say but will you be able to explain them or understand their response easily is a different story altogether.
if you would ask me that based upon the dozen or so trips that i have made along this route what is the one thing that i have to suggest... then my response would be do not try to go in one go unless it is absolute necessary.. and if you have to then leave lahore at maghrib and after taking breakfast at Cafe sajawal near Sadiqabad cross kot sabzal to enter sindh after 7am.