What I wanted to do is that I had multiple tables and/or images of different heights and wanted them positioned on the page side by side, so that the tops of the objects were aligned.
I couldn't figure this out, it didn't matter whether I put these 'in-line' or in separate Boxes (Minipages) (that seemed to be aligned the way I wanted in the editor), in output Lyx always seemed to align these objects somehow around the center of their height and not the top.
Finally, (after several hours of googling and trying to figure this out) I have the answer, so I'm posting it below, because I hope someone like me will find it useful in the future.