Subroutines and method calls don't interpolate inside strings or regexes. However, there's a common trick for interpolating an arbitrary expression inside a double-quoted string, that will work just as well in a regex:

"@{[ reverse 1 .. 3 ]} go!"   # reverse 1 .. 10 is in list context
"2 + 2 = ${\( 2 + 2 )}";      # 2 + 2 is in scalar context
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So, you could write your regex in one of these ways:

/^[a-z]{@{[ WORD_LENGTH ]}}$/i
/^[a-z]{${ \WORD_LENGTH }}$/i
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Although they might be hard to read... :)