labspace[l, a, b, i, cs_] := Block[{}, (List @@ ColorConvert[ColorConvert[LABColor[{l, a, b}], cs], "LAB"])[[i]]];
lmindata =
NMinimize[{labspace[l, a, b, 1,
"HSB"], (-1 <= l <= 2) \[And] (-3 <= a <= 9) \[And] (-6 <= b <=
2)}, {l, a, b}, AccuracyGoal -> 3, PrecisionGoal -> 3];
Print[lmindata];
... lots of errors follow
Is NMinimize not the correct choice, or ?