There's no actual option to disable browsing, but if you go to LW's tools > options > chat > untick the box to enable chat > apply > ok that should help. Having chat enabled seems to make it much easier to browse someone.

Just remember...a lot of people still think that if they can't browse a host, that host's not sharing So you might find that people add you to their list of blocked hosts, or kill your uploads, because they think you're a freeloader!