Go to
http://www.last.fm/listen/user/USERNAME/personal?share=1
Where USERNAME is your personal last.fm username. Copy the embed code underneath the flash player.
The embed code will look like this.
<object width="340" height="123"><param name="movie" value="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" /><param name=FlashVars value="viral=true&lfmMode=radio&radioURL=lastfm://user/USERNAME/personal&restTitle=USERNAME's Radio Station " /><param name="wmode" value="transparent" /><embed src="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" width="340" FlashVars="viral=true&lfmMode=radio&radioURL=lastfm://user/USERNAME/personal&restTitle=USERNAME's Radio Station " height="123" type="application/x-shockwave-flash" wmode="transparent" /></object>
Now, create a Custom User Profile field, Single-line text box. Name it Last.fm Username. (Make sure Field required is set to "No," and Editable by User is set to "Yes", in case your users don't have last.fm.)
Hit "Save", then go to the User Profile Field manager and take note of the fieldXX, e.g. field16.
Now replace all instances of USERNAME in the embed code with $userinfo[fieldXX]:<object width="340" height="123"><param name="movie" value="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" /><param name=FlashVars value="viral=true&lfmMode=radio&radioURL=lastfm://user/$userinfo[fieldXX]/personal&restTitle=$userinfo[fieldXX]'s Radio Station " /><param name="wmode" value="transparent" /><embed src="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" width="340" FlashVars="viral=true&lfmMode=radio&radioURL=lastfm://user/$userinfo[fieldXX]/personal&restTitle=$userinfo[fieldXX]'s Radio Station " height="123" type="application/x-shockwave-flash" wmode="transparent" /></object>
Put this code in your MEMBERINFO template wherever you want. I don't know your MEMBERINFO layout, so I really can't help with the HTML.
But it will look something like this. <if condition="$userinfo[fieldXX]">
<tr>
<td>
<object width="340" height="123"><param name="movie" value="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" /><param name=FlashVars value="viral=true&lfmMode=radio&radioURL=lastfm://user/$userinfo[fieldXX]/personal&restTitle=$userinfo[fieldXX]'s Radio Station " /><param name="wmode" value="transparent" /><embed src="http://static.last.fm/webclient/41/defaultEmbedPlayer.swf" width="340" FlashVars="viral=true&lfmMode=radio&radioURL=lastfm://user/$userinfo[fieldXX]/personal&restTitle=$userinfo[fieldXX]'s Radio Station " height="123" type="application/x-shockwave-flash" wmode="transparent" /></object>
</td>
</tr>
</if>