Lieutenant Locke possesses high level of health and strong shielding, and has access to Tech Armor ability, which he will use when his shields have been depleted. He also comes with several Blue Suns including a pair of heavies. Locke often takes cover behind a crate while his heavies take up your attention.
Lieutenant Locke is essentially a stronger version of the Blue Suns Centurion. As with those enemies, hit Locke from a distance with weapons and powers to take down his shields. Once those are gone, Locke should go down quickly. During the fight, be sure to watch for any other Blue Suns enemies, as their firepower combined with Locke's can make rushing in a costly maneuver. If possible, eliminate them before focusing on Locke.