The civics of 2009, 2010 has the rough, slow start problem even as a new car.
Google it and you will see many complaints about the same problem.
My civic has about 10,000 miles.
It happens a couple of times a week that the car starts tu-tu-tu-tu-tu-tu-tu-tu-tu-tu-tu-tu-wuuuun.
Sometimes the first start eventually fails and need to restart.
I have been having this problem since the first week I bought it new.
I also have a 2010 civic lx-s and have also had the same problem.
I took it into the dealership 3 times and feel like I got the run around about it.
Now the car has 23000 miles and went to start it and leave the store the check engine light came on and the transmission would slam into 2nd gear and would not shift into a higher gear.
getting the runaround from honda and the warrenty company.
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