The problem is simple, on the surface, because LaTeX has an internal command \verbatim@font to select the font for verbatim text. So
\makeatletter \renewcommand\verbatim@font{\normalfont\itshape}
Some nuance arises on the more traditional versions of LaTeX where the default fonts have some characters missing or rearranged; it is called the "OT1" font encoding, where "O" is for "old" or "original". So, if you are running lualatex or xelatex, the one line setting above is sufficient. If you are running latex or pdflatex, you need to change the font encoding, probably with
\usepackage[T1]{fontenc}
Another idiosyncrasy is that the underscore character in many fonts looks too wide, at least to my eyes.
Also something about your question with \verb |x_LT|. That may give an error because it will use the space character for quoting the argument. You should use \verb|x_LT|.
\verbthe whole point of\verbis that no latex command are active there. To get a_you can use\_– David Carlisle Apr 20 '20 at 21:11\textitbetter than\emphhere – David Carlisle Apr 20 '20 at 21:18\textitthen – Hrish Desai Apr 20 '20 at 21:31listingspackage provides one way. See e.g. How to format an inline source code and Emphasizing words within a string using the listings package in LaTeX for some examples. – Alan Munn Apr 20 '20 at 21:41\texttt,\emphand\textit-- and\verbinstead of placing the material in question into math mode, e.g.,$x_{LT}$? Please peruse any Intro-to-LaTeX tutorial to familiarize yourself with the basics of text and math mode. – Mico Apr 20 '20 at 21:51verbatim(when I look at the accepted answer). As such, this is a duplicate of Change font size of the verbatim environment. – Werner Apr 21 '20 at 04:22\verbunrelated to the other question. Please re-open. – Donald Arseneau Apr 21 '20 at 23:52\verbitalic' and 'how to make\verbsmall' are not exact duplicates, but they are very close. Additionally, the solutions are the same (modify\verbatim@font). Therefore, it makes sense to close, even if the discussion and the answers bring up additional relevant details. As Stack Exchange founder Jeff Atwood puts it: – Marijn Apr 22 '20 at 08:06\verbsmall, but the verbatim environment. Three of the four answers suggest different environments, which are inappropriate here. Changing the font size also has different ancillary considerations from changing font entirely, but there are many questions on shrinking verbatim environment font, not closed.... That said, I found a close match to this one: how-to-globally-set-verb-font-style-to-match-the-default-document-style, but it did not pop out of search easily! – Donald Arseneau Apr 22 '20 at 09:25