How to Italicize a Lettrine Letter Using the Goudy Initialen Font

I am using the Goudy Initialen font in a document. When the first sentence of a chapter is italicized, I would like to italicize the lettrine letter as well. This seems not to be a big deal for other fonts, but I have so far not been able to accomplish this.

Consider the code

documentclass{book}
usepackage{lettrine}
usepackage{xcolor}

input GoudyIn.fd
newcommand*initfamily{usefont{U}{GoudyIn}{xl}{n}}

begin{document}
thispagestyle{empty}

large

renewcommand{LettrineFontHook}{itshape}
renewcommand{LettrineTextFont}{itshape}

lettrine[lines=3]{color{red!80}initfamily{T}}{color{red!80}textbf{his}} textit{color{red} is the first sentence in the paragraph. I'd like, if possible, to italicize the `T' within the box.} This is a sentence in the paragraph. This is another sentence in the paragraph. This is another sentence in the paragraph. This is another sentence in the paragraph. This is another sentence in the paragraph. This is another sentence in the paragraph.
end{document}

The output is

I am trying to mimic the successful approach suggested by

How to italicise lettrine font

but it does not seem to work when using the Goudy font.

QUESTION: It it possible to italicize the letterine letter when using the Goudy Initialen font; and if so, I may I do that?

Thank you.