Lestrade's not exactly a well-rounded character: he mostly appears in just "The Boscombe Valley Mystery" and "The Noble Bachelor," and mainly only to prove how skilled and versatile Holmes is. Lestrade is an official police officer (one of three named officers who appear in these stories, along with Inspector Bradstreet and Peter Jones) and is a self-proclaimed "skeptic" (Valley.146) of Holmes's methods. It's Lestrade who's convinced, in the Boscombe Valley case, that James McCarthy is the murderer, and in the Noble Bachelor case, that Flora Miller has murdered Hatty Doran.
Lestrade is living proof of why it's a good thing that Holmes can operate outside of the law: the inspector's not a bad guy, by any means. But the pressures of "[having] to deal with a hard-headed British jury" (Valley.146) make Lestrade all too willing to accept surface appearances for the sake of easily "solving" and finishing a case. In many of these adventures, there's an undercurrent of suspicion over the institutions of The Law that fail to take into account individual circumstances or unexpected discoveries. Holmes, because he is a private detective, can choose whether to pursue a criminal or not (see "The Blue Carbuncle"). Lestrade has no such choice, and it makes him a poorer detective as a result.