Pop off the interior door panel, and tighten all of the internal screws, then lube with a silicone based spray lube.
I had a similar problem with my passenger side door handle. The insides just came loose.
White 2001 ZX3
17" FRPP White Rally Wheels, KW Cup Kit (1.6"), Progress 22mm Rear Sway, Short Ram Intake w/K&N Cone, Steeda 65mm TB, Ported 2k Manifold, FRPP 9mm Wires, MAC UDP, Clear Markers, OBX 4-1 Shorty Header, OBX ORP, FS Flex, 2nd Gen. MBRP Exhaust, FS/SCT Multi Chip