Quote Originally Posted by wysota
Does the same happen if you copy all your executables and libraries to a bare ubuntu VM ...?
Unknown. The deliverable must install on bare Ubuntu distro so, unless I'm going to try to DIFF two VMs completely, one bare and one with Qt installed, I don't know how much it would help.
It will quickly determine whether the missing dependency, if there is one, is a Qt component or an external component. The first is fixed by getting your deployment package's minimal Qt content right, the second by bundling external dependencies that are missing on your vanilla target.

If you want to know what the QtWebEngine library is directly dependent on then run ldd (or lddtree) against the .so file. Here is the example for your other library:
Qt Code: 
  1. $ ldd libQt5WebChannel.so
  2.         linux-vdso.so.1 (0x00007ffc9a5c4000)
  3.         libQt5Qml.so.5 => /home/chrisw/Qt/5.4/gcc_64/lib/./libQt5Qml.so.5 (0x00007fb20c786000)
  4.         libQt5Core.so.5 => /home/chrisw/Qt/5.4/gcc_64/lib/./libQt5Core.so.5 (0x00007fb20c047000)
  5.         libstdc++.so.6 => /usr/lib/gcc/x86_64-pc-linux-gnu/4.8.4/libstdc++.so.6 (0x00007fb20bd43000)
  6.         libc.so.6 => /lib64/libc.so.6 (0x00007fb20b9ab000)
  7.         libQt5Network.so.5 => /home/chrisw/Qt/5.4/gcc_64/lib/./libQt5Network.so.5 (0x00007fb20b645000)
  8.         libpthread.so.0 => /lib64/libpthread.so.0 (0x00007fb20b42a000)
  9.         libm.so.6 => /lib64/libm.so.6 (0x00007fb20b129000)
  10.         libicui18n.so.53 => /home/chrisw/Qt/5.4/gcc_64/lib/./libicui18n.so.53 (0x00007fb20acdd000)
  11.         libicuuc.so.53 => /home/chrisw/Qt/5.4/gcc_64/lib/./libicuuc.so.53 (0x00007fb20a952000)
  12.         libdl.so.2 => /lib64/libdl.so.2 (0x00007fb20a74e000)
  13.         libgthread-2.0.so.0 => /usr/lib64/libgthread-2.0.so.0 (0x00007fb20a54c000)
  14.         librt.so.1 => /lib64/librt.so.1 (0x00007fb20a344000)
  15.         libglib-2.0.so.0 => /usr/lib64/libglib-2.0.so.0 (0x00007fb20a00e000)
  16.         libgcc_s.so.1 => /usr/lib/gcc/x86_64-pc-linux-gnu/4.8.4/libgcc_s.so.1 (0x00007fb209df8000)
  17.         /lib64/ld-linux-x86-64.so.2 (0x00007fb20cfb8000)
  18.         libicudata.so.53 => /home/chrisw/Qt/5.4/gcc_64/lib/./libicudata.so.53 (0x00007fb208770000)
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If you want to know what is loaded in a running process you might like to try pldd (if it is available).