The two had engaged in a war of words through the media after a season long row which started whent he two sides met in September.
When Laws refused to shake hands with Alexander following Saturday's 5-3 defeat at Sincil Bank he promted some sharp criticism from Laws, but both men now say that they have buried their differences.
Keith Alexander said: "Brian and I have said some things that we maybe shouldn't have said.
"He has been man enough to come and shake my hand and we'll leave it at that."
Brian Laws said: "I have to hold my hand up and say congratulations to Lincoln."