You are absolutely right: paml software is requires qt4 not the qt5, which included to Ubuntu 18 and 20.
I consulted with IT-specialists and got the decision, which is very close to yours:
1) install qt4-devtools (because I need not only libs)
2) qmake-qt4 (because qmake has changed for qt5 too)
3) make
4) ./pamlX
After these four steps I have got pamlX and enjoy GUI interface.
Thanks for recommendation of
EasyCODEML, I am going to try it too.