Lyases catalyze reactions in which something adds to a double bond or in which a double bond is formed. Ligases form C-C, C-S, C-O, or C-N bonds by condensation reactions. Are you trying to find which enzymes are ligases or which are lyases?
ETA
It seems to me you must mean lyases. Lyases can cleave C-C, C-O, C-N, and other bonds.