I will be traveling in Lithuania, Poland and perhaps the Ukraine in a
few weeks and was wondering if there are any programs (government or
private) that allow visiting attorneys to meet attorneys in any of
these countries and observe some of their justice system.

This site has the Lithuanian and Polish Bar Associations:

http://www.hg.org/euro-bar.html

And here for The Ukraine:

http://www.brama.com/law/bar-lawyers.html


This one is much more extensive, but perhaps you have a special
interest, perhaps information from an appropriate US association could
help you:

http://www.megalaw.com/orgs/orgs.php#international