Hi there, I think I've rectified the issue, at least on my end. See the newly recorded video without lag here (
https://youtu.be/H2DkK-8xPjQ) and let me explain the steps below:
1. Launch Halo first and then Bandicam (the latest version 5.3.1.1880).
2. In Bandicam select the game recording mode (and allow it to run as admin). If you go back to the game, you should now see the fps in the upper left corner (or wherever you've defaulted it to).
3. Now, I'm assuming you have dedicated graphics (Nvidia in this case). What you want to do is change your video defaults in Bandicam, so it uses H264 Intel Quick Sync to record, not the Nvidia NVENC. My guess is because the Nvidia card is busy trying to run the game, it lags a lot when you also use it to record gameplay, hence me telling you to try the Intel option.
Let me know if this works!