The easiest way to perform what I want is finally to use the web service integrated into Livelink. Because there is really not much information on the Web about the whole Livelink API (that's surprising considering all we can find on Google these days), I'm willing to post here my solution. That's in fact really easy.
All I had to do is to install some add-on to Firefox (I used Fox but others would do the job too) to see the HTTP headers/packets when doing some work in Livelink. Most of the times, operations are done with the POST method. I realized with the Fox plugin that 3 POST are sent, the 2 first returned a 401 error while the 3rd returns the right 200 response and got the action done.
Then, I can deduce that Livelink is a SOAP-service based on a NTLM authentification. It looks like it has been developped in ASP.net.
To use the webservice within VBA, nothing more easy. You will need the Microsoft XML v6.0 livrary for the MSXML2 object, and there you go:
Dim sMsg As String
Dim sURL As String, postData As String
Dim ObjHTTP As Object
Set ObjHTTP = New MSXML2.XMLHTTP
sURL = "http://server.com/livelink/livelink.exe"
postData = "your-post-data"
ObjHTTP.Open "Post", sURL, False
ObjHTTP.setRequestHeader "Content-Type", "application/x-www-form-urlencoded"
ObjHTTP.send (postData)
Set ObjHTTP = Nothing
As simple as that, just find the right POST data with some kind of browser's plugin and you got it. Most of the post-data isn't encoded and easy to deal with.