You can insert a minipage environment with Insert -> Box -> Frameless. To insert a subfloat you do Insert -> Float -> Figure inside an existing figure float. To make a similar arrangement to what you're asking, the basic steps are:
- Insert -> Float -> Figure.
- Move cursor to before the caption of this figure, and add a
minipage with Insert -> Box -> Frameless.
- Open the settings of the minipage by right clicking the header or title, or whatever you want to call it, of the minipage (where it says Box (Minipage) and selecting Settings.
- Set the width to for example 47% of the Column width (or Line width). (If you don't want any space between the minipages, you can use 50%.)
- For the alignment, set the vertical alignment of the Box to Bottom. Close the settings.
- With the cursor inside the minipage, use Insert -> Float -> Figure (or the button on the toolbar) to insert a subfloat.
- Move the cursor outside the minipage. Don't make a new line, just have the cursor just to the right of it.
- If you made the minipage <50%, do Insert -> Formatting -> Horizontal Space, and choose Horizontal filling for the space.
- Add a second minipage as in step 2 and 3.
- Inside this minipage, add two subfloats with a paragraph break (hit enter) between them.
Depending on the size of the images, you may want to horizontally center them, which you do in the usual way, by adjusting the paragraph settings inside each subfloat.
Note I did this in an old version of LyX, I can't guarantee that it's identical in the latest one. This is what it looks like here, with \rule{<width>}{<height>} instead of images.
