Use flash media live encoder
From Livestream » User Guide
Livestream integrates directly with Adobe Flash Media Live Encoder (FMLE) to allow you to broadcast live to your Livestream channel. FMLE is now available for PC and Mac users.
Download it free from Adobe by clicking here
Using Flash Media Live Encoder with Livestream
Stream to Flash Media Server
In order to broadcast to Livestream using FLME you will need to check the "Stream to Flash Media Server" box and configure the FMS URL and stream name as below:
FMS URL: rtmp://publish.livestream.com/mogulus/channelname/username=yourusername/password=yourpassword/isAutoLive=true/false
Stream name: livestream
Depending on your computer specs and connection speed you can customize the encoding settings for best quality.
You can find here Encoding Profiles for Low, Medium, and High quality profiles.