I'm a bit late to the party, but if you just want to make sure the \LaTeX command expands correctly without kerning adjustments (which you can do with the metafont package), you can force the command to use the Computer Modern font family.
To achieve this, you redefine the command from where you want to apply it:
\let\myLaTeX\LaTeX
\def\LaTeX{\fontfamily{cmr}\rmfamily\selectfont\myLaTeX}
You can as easily revert this back to normal by doing:
\let\LaTeX\myLaTeX
after the \LaTeX you need to typeset occurs.
so the following:
% .... %
\vspace*{2mm}
\let\myLaTeX\LaTeX % <- Copy \LaTeX here
\def\LaTeX{\fontfamily{cmr}\rmfamily\selectfont\myLaTeX} % <- Redefine here
{\Large\mdseries\textsc{The logo with Computer Modern:}\par}
{\Huge\LaTeX\par}
\let\LaTeX\myLaTeX % <- Revert changes
{\Large\mdseries\textsc{The logo with default font:}\par}
{\Huge\LaTeX\par}
\vspace*{2mm}
% .... %
Will produce something like this:

Explanation
- The
\let\myLaTeX\LaTeX command will copy \LaTeX into \myLaTeX, we do this to avoid overwriting the command \LaTeX in the next step. Think of it as "\let \this be the same as \that"
\def\LaTeX{...} redefines the \LaTeX command sequence with whatever is entered inside the brackets {...} (know as a group).
{\fontfamily{cmr}\rmfamily\selectfont\myLaTeX} sets the font cmr on what follows, in our case, the previously \let (or copied) command sequence \myLaTeX. Note: I've specifically set \rmfamily here to avoid warnings of undefined shapes in some fonts.
This can also be done with some of \TeX and friends in the same way.
For the entire document
If you want to use this for every macro, you can put the definition in the preamble of your main *.tex file, as in the MWE below:
\documentclass[11pt]{article}
\usepackage[light, default]{sourcesanspro} % <- Using this sans serif
\usepackage[T1]{fontenc}
\let\myLaTeX\LaTeX
\def\LaTeX{\fontfamily{cmr}\rmfamily\selectfont\myLaTeX}
\begin{document}
\thispagestyle{empty}
\begin{center}
\vspace*{\fill}
\noindent\rule{\textwidth}{1pt}\par
\vspace*{2mm}
{\Large\mdseries\textsc{This Document is typeset with}\par}
{\Huge\LaTeX\par}
\vspace*{2mm}
\noindent\rule{\textwidth}{1pt}\par
\vspace*{\fill}
\end{center}
\end{document}
I generally recommend doing this over making inline changes to fonts. And since LaTeX traditionally is typeset with roman font, I think it should be eaten as intended. Even so, I've added a few options further down.
Result
To illustrate how this works, I use the Source Sans Pro font family as the document font (like I did in the example above). This font does not expand \LaTeX well (in my opinion), as shown below:

And here is how it will look once you force the font for \LaTeX:

Other options
If you want to use the same font type for consistency, you can use a font that \LaTeX expands well with:
For Typewriter fonts, try pcr (Courier), which looks like this:

For Sans Serif fonts, try phv (Helvet), which looks like this:

For Serif fonts, you can also try ppl (Palatino), which looks like this:

Further reading
- How to typeset every TeX related logo
- The difference between local and global scope
- Changing the font of specific words or paragraphs (LaTeX), (XeLaTeX & LuaTeX)
{\setmainfont{Times-Roman}\LaTeX}? – TeXnician Sep 19 '18 at 19:26\setromanfontis the outdated equivalent of\setmainfontand you override your roman font by making Fira Sans the main font. Alternatively you can do\newfontfamily\myfont{Times-Roman}in the preamble and do{\myfont\LaTeX}. – TeXnician Sep 20 '18 at 06:02