A federal magistrate judge recommended the dismissal of a lawsuit that accuses Reed Smith LLP and Clark Hill PLC of using baseless lawsuits, discovery delays—and even thuggish private eyes—to help a client conceal its criminal activities.

The May 17 recommendation could bring an end to one of several high-stake lawsuits that LabMD Inc. is pursuing against cybersecurity firm Tiversa Inc. and some of the nation’s largest law firms.

LabMD claims that Tiversa hacked its computers to steal a file with...