You use likewise when you are comparing two methods, states, or situations and saying that they are similar. All attempts by the Socialists to woo him back were spurned. Similar overtures from the right have likewise been rejected = similarly
in like or similar manner; "He was similarly affected"; "some people have little power to do good, and have likewise little strength to resist evil"- Samuel Johnson
If you do something and someone else does likewise, they do the same or a similar thing. He lent money, made donations and encouraged others to do likewise