Your video must align with FB Live requirements to be streamed properly. If it is not you can compress/encode it using this tutorial.
The easiest way is to use a tool like this: VideoProc
You just need to upload a video file and it'll compress it automatically.
If the first solution doesn't work or you want more option to configure compression settings you can use Handbrake.
Here is step by step guide how to do it:
Install Handbrake by choosing the version for your operating system from http://handbrake.fr/
Open your video file in Handbrake
Choose Format MP4 file.
For Video Codec choose H.264 (x264).
Enter an Average Bitrate (kbps) for the video to be 4,000
Hit the Start button and wait until the video has finished encoding.
Handbrake will let you know when it has finished.