Lateral entry is not applicable for government engineering colleges that follow the JAC Delhi admission process. So NSUT does not allow lateral entry for any of the B.Tech branches, including Civil.
On the other hand, PTU has the provision of lateral entry into Civil Engineering. But the requirement for the same is a polytechnic diploma in Civil.
I am not much aware of the procedure of NSIT Dwarka. But lateral entry in Civil Engineering is allowed at PTU. However, you will need to have a Polytechnic Diploma in Civil Engineering.
You cannot take lateral admission at NSIT because there is no civil engineering branch at NSIT. In addition to that, no government college that follows the JAC admission process allows lateral admission.