Converted to html with MathJax

In equation environment, click the button Insert plain text(Alt+$). Type space twice to insert a quad space.
In preference > convert, turn on “Export mathematical formulas as MathJax” and export to HTML:
and open the exported HTML in browser. It displays as
The exported LaTeX code is \displaystyle a \text{\quad a}
Because MathJax doesn’t support text macros (See this issue) it output \quad in \text verbatim.
also with \textbf,\textrm,\textit,\textup
Macros inside \mathrm such as \quad will display properly:
a \mathrm{\quad a}

Here is probably also the case to submit a bug report at