Lawlar (wrist) took on-field batting practice last week, Alex Weiner of ArizonaSports.com reports.
Arizona manager Torey Lovullo said Lawlar felt good following the batting-practice session, though the skipper doesn't believe the infielder is ready for game action. Lawlar is eligible to return from the 60-day injured list June 2, but he'll likely need additional time beyond that to recover from his fractured right wrist before being activated.