Is it advisable (or even usual) to invite a foreign member of doctoral jury to give a lecture just after the defense? Or is it inappropriate? I will have my doctoral defense next month, in Italy. In my jury there's a foreign member, who comes on purpose from Belgium (I know him in person and I invited him to be member of the jury, through my supervisor).
I had two opposite advices.
Somebody told me that it is usual, in this situation, to invite the foreign member to give a lecture at my Department, after the defense (in the afternoon). They say that it is a great occasion, and that he would happy of doing it (or, even, he would be upset if not invited).
Somebody else told me that it is not polite, that he could feel forced and that, after the discussion, maybe he would like just to go around the city and relax.
I think it is appropriate to invite an academic to give a lecture on their work at any point, provided the invitation is politely conveyed.  Part of politely conveying an invitation is making the invitee feel comfortable declining it.  

I can think of certain situations in which it is arguable that without further personal knowledge of the invitee, the invitation itself exerts an impolite pressure to accept: e.g. if you invite a job candidate to give an "extra lecture."  But I don't see why a foreign jury member would feel compelled to give an extra lecture in this situation.  Unless you know of some specific plausible reason why he would feel pressured to do so, I think it is absolutely permissible to invite him.  Since you are a bit concerned about this, I would mention in the invitation itself that the invitee can freely decline, in a way which suggests that he will not be committing any kind of social error by doing so.  Especially if you know this person, um, in person, I see no problem here.

General tip for dealing with human beings: when possible, try not to assume that they will want to do X or that they will not want to do X.  Develop enough social skills so that you can ask them which one it is.  Of course some exceptions apply...