1
\documentclass[11pt,letterpaper]{memoir}
\usepackage{lipsum}
\usepackage{type1cm}
\usepackage{lettrine}
\setcounter{DefaultLines}{2}
\renewcommand{\DefaultLoversize}{0.14}
\renewcommand{\LettrineTextFont}{\relax}

\begin{document}
    \lettrine[]{\textbf{D}}{ rop caps }\lipsum[1]
\end{document}

But when I add the commands from http://www.tug.dk/FontCatalogue/royalinitialen/ the drop cap changes into an ordinary non-bold font instead of the decorated Royal Initialen:

\documentclass[11pt,letterpaper]{memoir}
\usepackage{lipsum}
\usepackage{type1cm}
\usepackage{lettrine}
\setcounter{DefaultLines}{2}
\renewcommand{\DefaultLoversize}{0.14}
\renewcommand{\LettrineTextFont}{\relax}

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

\begin{document}
    \lettrine[]{\textbf\initfamily{D}}{ rop caps }\lipsum[1]
\end{document}

What am I doing wrong?

2

The problem is \textbf that is completely out of place and just acts on \initfamily: you're essentially saying

\textbf{\initfamily}D

which of course doesn't typeset D in the expected font. Besides, the family has just a single weight, so using \textbf will do nothing anyway.

I modified the code also using proper lettrine methods.

\documentclass[11pt,letterpaper]{memoir}
\usepackage[T1]{fontenc}
\usepackage{fix-cm}
\usepackage{lipsum}
\usepackage{lettrine}

\setcounter{DefaultLines}{2}
\renewcommand{\DefaultLoversize}{0.14}
\renewcommand{\LettrineFontHook}{\usefont{U}{RoyalIn}{xl}{n}}
\renewcommand{\LettrineTextFont}{}
\setlength{\DefaultFindent}{\fontdimen2\font}

\input{RoyalIn.fd}

\begin{document}

\lettrine{D}{rop caps} \lipsum[1]

\end{document}

enter image description here

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