The answer is you probably can use your original shock absorbers with lowering springs. With some provisos
First of all, check with the manufacturer of the lowering springs you are considering and ask them if you can use your original shock absorbers with their springs.
In my experience, 99 times of a 100, if the lowering springs you want lower the car by 35mm or less, there will be no problem.
Should you fit lowering springs with the original shock absorbers?
Depends on where you live and what the roads are like. Also it depends on what you are prepared to put up with comfort wise and what wheels and tyres you are using.
In my opinion, if you use your car on road 99% of the time, and even if the roads where you are are smooth. I think I would go for the sport springs with the original dampers.
In my experience, the increase in performance from changing to “sport” shocks is not big and for the decrease in ride comfort and the associated cost, sport dampers are not worth it.
Good quality lowering springs like H&R or Eibach with the car’s original shock absorbers will give the car all the stability you could probably ever need on the road with the bonus being, ride comfort is almost the same as with the car’s original springs.
In short, good quality lowering springs on their own give you the best of all worlds.
Better performance (read stability)
Close to stock ride comfort
And also the cheapest way of upgrading your suspension