We are trying to fly the drone in an indoor environment. In order to navigate we required a drone heading, we only have an accelerometer, gyro and Velodyne ( no magnetometer, no GPS) as a source. So how we can calculate drone heading using only these sources?
First update to ArduCopter 4.3.0
The version you are using is very old and limited.
Sorry its type error ,we have already use 4.3
Have you taken a look at the apsync companion computer?
Yes, we did use a similar setup. There is PI 4 connected to USB of Cube black. This PI has mavproxy running inside and then routed the data to use it on ROS. We can feed the orientation via NMEA strings and set EK3_SRC1_YAW to GPS. The only problem here is if we disable the compass then the GPS-type navigation functionality is gone since our assumption is it requires true north heading. Is there any documentation on how this GPS navigation work internally in ardupilot firmware?
So basically it is a SLAM configuration, using the rotating Lidar to build a map and navigate
Correct. We want to inject localization data of LIDAR via GPS hardware port and then give navigation coordinates via mavlink.
WIKI is your friend 
Here is an example of ROS Cartographer implementation with ArduPilot
https://ardupilot.org/dev/docs/ros-cartographer-slam.html