About half way through the season, he has a defensive WAR of 3.4. The current record is 5.4 by SS Terry Turner in 1906. The only other season with 5 or higher is 5.1 by Art Fletcher (SS) in 1917.
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Update: After the July 3 game, he is up to 3.5. That is tied for the 51st best fielding season ever. If he stays on this pace, he would end up with 7.0, beating the old record by 29.6%. It looks like he had 5 assists and a putout last night. In his career he now has a defensive WAR of 5.1 in just 120 games. The single season record for a 3B man is 4.5 by Brooks Robinson in 1968. It looks like Lawrie is already in the top 10 seasons for 3B men.
"The Book" blog had an interesting discussion of Lawrie's defense in May. Part of it has to do with where he stands when the Blue Jays put on a shift, which can affect hs stats. See Has Brett Lawrie ALREADY saved 14 runs so far this year?