What are the example reactions catalyzed by a ligase or a lyase?

Ligases catalyze the formation of covalent bonds between molecules, resulting in the joining of two molecules. DNA ligase joining Okazaki fragments (short, newly synthesized DNA segments on the lagging strands) during DNA replication is a classic of a ligase-catalyzed reaction. 

Lyases catalyze reactions that cleave or add chemical groups within molecules, which leads to the breaking of existing bonds or the creation of double bonds. The hydration of carbon dioxide to form bicarbonate by carbonic anhydrase is an example of a lyase-catalyzed reaction.