Yep, LW will have to be connected if uploads are going to continue.

What you can do is set your LW to shut down after transfers...that way, once the uploads in progress are done, LW will close
In LW go tools > options > system tray > tick 'shutdown after transfers' > apply > ok.

Don't worry too much - if you have to make a phone call & shut LW down before an upload's finished, the person can either finish their download from another source or they can wait until you're back online. It's great that you care about other peoples' downloads but if you have dialup then sometimes your phone call is more important than LW! Don't feel bad if you have to disconnect!

I don't know if you've seen this thread below, but it's a good guide for how to get the most out of LW with a dialup connection.
http://www.gnutellaforums.com/175733-post5.html