Adding empty lines for readability

Since LyX is attempting to show something that represents the output and not the raw LaTeX input, there isn't a way (that I'm aware of) to put extra spaces in the editor since that would imply having them in the output.

One thing you can do as a "dummy marker" is to insert an "ERT" box (Ctrl+L or Alt+I+X) on the line you want to preserve as empty. The ERT box is copied verbatim into the LaTeX source, so if you leave it empty, it will have no effect on the final document.

Alternatively, you could set the document to use vertical space to separate paragraphs rather than indents (Document > Settings > Text layout). Note that this will change your output as well as the LyX representation, but it's easy to change back when you're ready to export your finished document.

You can do what you want by adding the following to Document > Settings > Local Layout

Style Standard
    Category              MainText
    Margin                Static
    LatexType             Paragraph
    LatexName             dummy
    ParIndent             MM
    ParSkip               0.4
    Align                 Block
    AlignPossible         Block, Left, Right, Center
    LabelType             No_Label
    KeepEmpty             true
    FreeSpacing           true
    HTMLStyle
        div.standard {
            margin-bottom: 2ex;
        }
    EndHTMLStyle
End

KeepEmpty allows for multiple returns and FreeSpacing allows for multiple spaces. If you decide you want to make this change permanent, either create a layout and put it in your LyX user directory's layout folder or if you want it on a per-document basis, create a module.

All of this information and much more is in Help > Customization

this doesn't address LyX, which i'm nor really familiar with.

however, (la)tex interprets a blank line as a new paragraph. furthermore, paragraph breaks are not permitted within math, so will result in error messages.

you can simulate a blank line in your code by adding a line containing only a % sign at the beginning; this give a reasonable visual equivalent of a blank line.

(la)tex (except when explicitly set up in verbatim mode) interprets multiple spaces as a single space, so adding a few extra (keyed) spaces to provide a visual gap in the input is okay, and often a good idea, especially in strings of math, or to visually simulate column positioning in a table. beware, however, of wysiwyg input software that interprets multiple keyed spaces as indications that multiple spaces are wanted in output, and translates an "additional" keyed space to \ (backslash space) in the tex file; i don't know whether LyX does that, so you should check.