I followed your advice and it worked. Apparently the Qt5PrintSupport.dll and Qt5OpenGL.dll files were missing. I copied them to the application directory and it worked.
Thank you very much.
Shell config files such as ~/.bashrc, ~/.bash_profile, and ~/.bash_login are often suggested for setting environment variables. While this may work on Bash shells for programs started from the shell, variables set in those files are not available by default to programs started from the graphical environment in a desktop session
Out of personal experience I recommend also to ask your question on QWT mailing list
AFAIK QWT is still independent and only based on Qt libs. Uwe has been monitoring this forum in the past, but answers are potentially faster through QWT mailing list.