Does anyone know if it's possible to add more space between paragraphs
in the LyX user interface (i.e., not the output)?
Not exactly more space, but there's a --Separator-- in most layouts
(choose it where you choose paragraph styles: Standard, Section, Title...)
Along the same lines,
is it possible to add a margin in the user interface?
Yes. In Local Layout of Document Settings dialog; just type
Format 11
RightMargin MMMMMMM
LeftMargin MMMMMMM
press Validate
press Apply
If you don't find --Separator-- environment, you can also add it to the
Local Layout:
Style --Separator--
Category MainText
KeepEmpty 1
Margin Dynamic
LatexType Paragraph
LatexName dummy
ParIndent MM
Align Block
LabelType Static
LabelString "--- --- --- ---"
LabelFont
Color Blue
EndFont
End