There is a problem with high-resolution elevation data for Iraq, I did not hear about LiDAR data for this area. But, as I remember, there is a possibility to get 12x12m DEM for the entire world (and therefore also for Iraq) from TanDEM-X Science Service System, but only for scientific purposes. Just look on this webpage: https://tandemx-science.dlr.de/
If there are no lidar nor USGS elevation data for Iraq, you can deploy an Unmanned Aerial Vehicle (UAV) to your ROI to obtain your elevation data with centimetre resolution.