I have pulled the lathe and plaster off the brick wall and want to clean and finish the brick. Any suggestions for the easiest cleaning and what to coat it with?

Are you thinking of painting the brick or something? Many people keep the plain brick face. You can wire brush brick or sand blast with corncobb husks or even dry ice.

Thanks for the sand blasting tip, and no I am not going to paint it. I want to leave it exposed with probably a clear coat of some kind. Can the sand blast equipment be rented?

You can rent sandblasters but I'd recommend that you get some estimates too. Repeated exposure to silica sand can harm you if you don't use the proper equipment. A one time blasting might not harm you but why take the chance.