Hi. If I'm not mistaken, that's exactly how SHOUTcast/Icecast streaming works.
The streaming source encodes whatever music you have, and then streams the encoded material to the streaming server. Clients connect to the server to listen to music.
The streaming source will encode your lossless files on the fly before streaming them.
If you use Windows:
If you use Winamp2, and would like to stream MP3 streams, have a look at
the SHOUTcast docs. You'll need the SHOUTcast DSP for Winamp2, and the SHOUTcast server.
If you use foobar2000, and would like to stream Ogg Vorbis streams, have a look at
ODDSOCK.org. You'll need the oddcast2 DSP for foobar2000, and the Icecast2 server.
If you use *nix:
Have a look at
icecast.org. You can use icecast and ices to stream MP3, or icecast2 and ices2 to stream Vorbis.