ConTeXt does not load png file given by lua code

You add spaces in the output of your command at the begin and end of the definition.

\defineexpandable[1]\Background{
  \directlua{
    local cases = {
      "noise-blue.png",
      "noise-yellow.png",
      "noise-red.png",
      "noise-green.png"
    }
    tex.sprint(cases[#1])
  }
}

\starttext
“\Background{1}”
\stoptext

To get rid of the spaces you have to add a comment sign after the braces.

\defineexpandable[1]\Background{%
  \directlua{
    local cases = {
      "noise-blue.png",
      "noise-yellow.png",
      "noise-red.png",
      "noise-green.png"
    }
    tex.sprint(cases[#1])
  }%
}

\starttext
“\Background{1}”
\stoptext

You can also use the texdefinition environment to create the command which doesn’t convert the end of a line into a space.

\starttexdefinition Background #1
  \startlua
    local cases = {
        "noise-blue.png",
        "noise-yellow.png",
        "noise-red.png",
        "noise-green.png"
    }
    context(cases[#1])
  \stoplua
\stoptexdefinition

Alternative solution

A different way to create a index for your images is the \setvariables which you can use to assign a key to each image. The graphics can than be accessed with the \getvariable command.

\setvariables
  [background]
  [1={noise-blue.png},
   2={noise-yellow.png},
   3={noise-red.png},
   4={noise-green.png}]

\starttext
“\getvariable{background}{1}”
\stoptext

As an alternative to Wolfgang's answer and as alternative to your Lua solution, you might want to consider using \useexternalfigure which allows you to name figures.

\useexternalfigure[background:1][noise-blue.png]
\useexternalfigure[background:2][noise-yellow.png]
\useexternalfigure[background:3][noise-red.png]
\useexternalfigure[background:4][noise-green.png]

\starttext
  \externalfigure[background:1][width=4cm]
\stoptext