You could also use the glob built-in function although you may need to take care if your lists contain metacharacters significant to glob.

$ perl -le 'print for glob( q{{a,b}{c,d}} );'
ac
ad
bc
bd
$
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$ perl -le '
> @lists = (
>    [ qw{ 1 2 3 } ],
>    [ qw{ a b } ],
>    [ qw{ X Y Z } ],
>    );
> $globStr = 
>    join q{},
>    map { qq{{@{ [ join q{,}, @$_ ] }}} }
>    @lists;
> print for glob $globStr;'
1aX
1aY
1aZ
1bX
1bY
1bZ
2aX
2aY
2aZ
2bX
2bY
2bZ
3aX
3aY
3aZ
3bX
3bY
3bZ
$
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I hope this is helpful.