Lawrenson feels that Liverpool will sever ties with Suarez, as they look to move on next season.
"While the comments from Ian Ayre and Brendan Rodgers sought to dampen such speculation, they were as much to ensure the player's value doesn't decrease over the summer.
"Now Liverpool must be wondering whether he is worth all the aggravation.
"My view on the FA's decision to ban Suarez for 10 games for his bite on Branislav Ivanovic is that on appeal the Uruguayan may get it down to eight games.
"But we can't be that surprised, really. Suarez's list of misdemeanours is getting longer and longer and at some stage he is going to have to learn."