I had the same problem (Mandrake 9.0) even if qt3-devel was previously installed. Here is my solution if you decide to compile from rpm source.
As root, after downloading lyx-1.3.1-1-qt.src.rpm, in a terminal: ln -s /usr/lib/qt3 /usr/lib/qt QTDIR=/usr/lib/qt PATH=$QTDIR/bin:$PATH MANPATH=$QTDIR/man:$MANPATH LD_LIBRARY_PATH=$QTDIR/lib:$LD_LIBRARY_PATH export QTDIR PATH MANPATH LD_LIBRARY_PATH then the command rpm --rebuild lyx-1.3.1-1-qt.src.rpm will proceed correctly (it's long!) and the new rpm will be in /usr/src/RPM/RPMS/i586/ R. Ouellette -- Édité et transmis avec des logiciels libres sous Linux !
