Is it possible to send LiveMeeting invites from Java or C#? I'm mostly interested in a Java API.
Are there any open API's for LiveMeeting integration?
Well, a quick Google search of LiveMeeting API turns up this link.
More specifically, it looks like it is all XML based, so you should be able to call it from Java. Below is the closest to sending an invite that I could find.
Creating a Meeting Requesting the Text for an Invite in audienceInviteText/presenterInviteText in the FieldList
Creating a meeting through the Live Meeting API does not automatically generate meeting invitation e-mail. Instead, you can request the meeting invitation text to be returned in the CreateMeetingReply message. The returned text can be pasted into e-mail that you generate outside of the API. The text returned is the same text that is returned using Live Meeting Manager to create the meeting.
To receive the meeting invitation text in the reply to this request, audienceInviteText needs to be included in the FieldList. The following XML request is sent to the conference center.
The options audienceInviteText and presenterInviteText can only be included in the FieldList portion of a createMeeting request as the returned information is autogenerated by the conference center. The information returned through the reply can be included in an e-mail message, which the meeting creator can then send to the meeting audience/presenters for easy access to the meeting.
<PlaceWareConfCenter authUser="apiuser" authPassword="Pa$$w0rd">
<CreateMeetingRequest name="status" title="Tailspin Toys Status Meeting" maxUsers="25">
<OptionList>
<TimeOption name="startTime" value="2006-12-01T18:00:00Z" />
<DecimalOption name="duration" value="1800" />
<StringOption name="audiencePassword" value="auPa$$w0rd" />
<StringOption name="presenterPassword" value="prPa$$w0rd" />
</OptionList>
<FieldList>
<Name>audienceInviteText</Name>
<Name>presenterInviteText</Name>
</FieldList>
</CreateMeetingRequest>
</PlaceWareConfCenter>
The following code shows the XML reply.
<PlaceWareConfCenter>
<CreateMeetingReply>
<MeetingReply>
<OptionList>
<StringOption value="Jeff Hay has invited you to attend an online meeting using
Microsoft Office Live Meeting.

https://www.livemeeting.com/cc/contoso/join?id=name10&role=attend&pw=auPa%24%24w0rd



AUDIO INFORMATION
Audio has not been set up for this meeting.


FIRST-TIME USERS
To save time before the meeting, check your system to make sure it is
ready to use Microsoft Office Live Meeting. 
 http://go.microsoft.com/fwlink/?linkid=52354

TROUBLESHOOTING 
Unable to join the meeting? Follow these steps:
 1. Copy this address and paste it into your Web browser:
 https://www.livemeeting.com/cc/contoso/join
 2. Copy and paste the required information:
 Meeting ID: name10
 Entry Code: auPa$$w0rd
 Location: https://www.livemeeting.com/cc/contoso/join
If you still cannot enter the meeting, contact support:
http://r.office.microsoft.com/r/rlidLiveMeeting?p1=7&p2=en_US&p3=LMInfo&p4=support" name="audienceInviteText">
</StringOption>
<StringOption value="Jeff Hay has invited you to present an online meeting using
Microsoft Office Live Meeting.

 https://www.livemeeting.com/cc/contoso/xmlapi6/join?id=name10&role=present&pw=prPa%24%24w0rd



AUDIO INFORMATION
Audio has not been set up for this meeting.


FIRST-TIME USERS
To save time before the meeting, check your system to make sure it is
ready to use Microsoft Office Live Meeting. 
 http://go.microsoft.com/fwlink/?linkid=52354

TROUBLESHOOTING 
Unable to join the meeting? Follow these steps:
 1. Copy this address and paste it into your Web browser:
 https://www.livemeeting.com/cc/contoso/join
 2. Copy and paste the required information:
 Meeting ID: name10
 Entry Code: prPa$$w0rd
 Location: https://www.livemeeting.com/cc/contoso/join
If you still cannot enter the meeting, contact support:
http://r.office.microsoft.com/r/rlidLiveMeeting?p1=7&p2=en_US&p3=LMInfo&p4=support" name="presenterInviteText">
</StringOption>
</OptionList>
</MeetingReply>
</CreateMeetingReply>
</PlaceWareConfCenter>