I think you misunderstood my issue: your Lua way does the same thing than my TeX way: it displays:

2 Cat

3 Mouse

but that is NOT what I want. What I want is:

1 Cool

2 Cat

3 Mouse

So I need to check if the chapter label has been set empty or not by the user, because it is not empty (let's say the user chose the string "CHAPTER~" for the chapter label) I want to display this:

CHAPTER ONE Cool

CHAPTER 2 Cat

CHAPTER 3 Mouse

The way to do that is to check if the variable \currentstructurelabel is empty, so the code must be:

\define[1] \MyCommand{\doifelse{\currentsectioncountervalue}{1}{\doifnotemptyelse{\currentstructurelabel}{ONE}{#1}}{#1}}

\setuphead[chapter][deepnumbercommand=\MyCommand]

\starttext

    \setuplabeltext[chapter=CHAPTER~]

        \chapter{Cool}

        \chapter{Cat}

        \chapter{Mouse}

\stoptext

\starttext

But the problem is that in the second case, even if the chapter label is set empty the command \doifnotemptyelse{\currentstructurelabel} thinks the variable \currentstructurelabel is not empty. So there must be something invisible in it, like a strut or something.