With normal use the mechanical connections in a table lamp can loosen, causing the lamp to lean or to become wobbly. Once you understand the simple construction of a table lamp, it is very easy to repair the wobbly lamp. Table lamps are essentially decorative elements and a light fixture threaded onto a long metal rod, with a nut at the bottom to hold the parts in place. With common tools, you can fix your wobbly lamp in minutes.
Unplug the lamp. Remove the light bulb and shade so they won't be damaged when you move the lamp base. Turn the lamp over to access the bottom of the base of the lamp. Lamp bases are usually covered with a felt material to protect furniture from scratches. Use the pointed tip of your scissors to make a hole in the felt, then cut the felt off the base to access the threaded rod and nut that hold the lamp together.
Check to see if the nut that holds the light fixture to the top of the lamp is secure. Tighten with an adjustable wrench, if needed. Do not overtighten, as this can crack a ceramic or glass lamp. Tighten the lower nut on the threaded rod, at the base of the lamp.
Place the lamp base on the felt. Trace around the base. Cut the new felt with scissors, 1/2-inch smaller in diameter than the traced line. Use all-purpose glue to attach the new felt to the lamp base and dry, per manufacturer's instructions. Reattach the shade and light bulb.