There is no straightforward way of moving a caption from left to right or vice versa. The package only allows for global settings, so the captions are always on the left or always on the right. For two page setups you can also have them always on the inner or always on the outer side. There are things you can try though:
Make the caption wider
It looks from your screenshot that the problem is more that the area for the caption is too narrow, making it overprint the table itself. Fixing this problem is very easy:
At the very start of the
SCtable float, add an ERT with Ctrl + L, and write
 in this. What this does is adding
 as an optional argument to the
SCtable environment, and that number is the relative width of the caption to the table. With
3 the caption can be three times the width of the table. Here is a screenshot from LyX with PDF output next to it:
Add an ERT just before the table, and write in that the following:
If you copy-paste, use Edit --> Paste Special (Ctrl+Shift+v) to paste the code in.
Just after the table, add a new ERT and add just a closing brace, i.e.
You can place captions next to tables without using
sidecap at all. Add a normal table float, and start by deleting the caption that is already there. Add a
minipage with Insert -> Box -> Frameless, and make that for example half the width of the line. Add the caption inside this box, with Insert --> Caption. Finally, add the table on the same line as the box (i.e., don't hit enter before adding the table).