pdflatex fonts in lualatex

The URW Grotesk font is only available as PostScript Type 1 font and can therefore not used via fontspec. However, the old font switching commands still work, when you also change the font encoding:

\newcommand{\fontcommand}[1]{{\fontencoding{T1}\fontfamily{ugq}\selectfont #1}}

This can be used with pdflatex and lualatex, e.g.:

\documentclass{standalone}
\usepackage{fontspec}
\newcommand{\fontcommand}[1]{{\fontencoding{T1}\fontfamily{ugq}\selectfont #1}}

\begin{document}
\fontcommand{The quick brown fox jumps over the lazy dog.}
\end{document}

Since you already have the Type 1 fonts, Ralf Stubner’s answer is likely to be more practical for you. However, URW Grotesk is a commercial font also available in TrueType and OpenType formats. Your company might have purchased the OpenType font, which you can use through the simple (but deprecated) commands

\usepackage{fontspec}

\defaultfontfeatures{Scale = MatchLowercase}
\setsansfont{URW Grotesk}

In this case, you would replace \fontfamily{ugq} with \sffamily. If this doesn’t work, you could use the newer interface:

\setsansfont{URWGrotesk}[
  UprightFont = *-Reg ,
  BoldFont = *-Bol ,
  ItalicFont = *-RegIta ,
  BoldItalicFont = *-BolIta ,
  Extension = .otf
]

Since the original template and perhaps other legacy documents refer to the NFSS font family, you could keep compatibility by adding the option, inside the square brackets, NFSSFamily = ugq. That should enable the command you gave to continue to work. You also could save a similar definition to a file named URWGrotesk.fontspec and use that to keep your source documents nice and simple. In this case, be sure to add Ligatures = Common inside the square brackets. This was the default for \setmainfont and \setsansfont, but needs to be specified for \newfontfamily.

Failing that, the closest free substitutes would be Helvetica clones such as Geneva, Arial, TeX Gyre Heros or Nimbus Sans.