An LG gas cooktop burner lights when the spark igniter beside it arcs and gas from the burner ports reaches that spark. Clicking without a flame means one half of that meeting is not happening: either gas is not reaching the spark, or the spark is not reaching the gas. Almost every cause is at the top of the range, in parts that lift off. There is one exception, and it is the first thing to rule out.
If You Smell Gas, Stop
A burner that has been clicking for a while may have released gas that did not light. If the smell is faint, turn the knob off and open a window, and do not attempt to light anything until the air is clear. If the smell is strong or does not fade within a minute or two, do not operate any switch, appliance or phone inside the house; leave, and once you are outside call your gas utility or 911. Do not troubleshoot a burner in a room that smells of gas. Everything below assumes the air is clear.
The Wet Igniter
The commonest cause follows cleaning or a boil-over. Water on the ceramic igniter or in the burner head shorts the spark and blocks the ports. Turn every knob off, unplug the range so no spark can occur while your hands are on the burner, lift off the grate and the burner cap, and let the head and igniter dry completely, which can take hours. A hair dryer on cool speeds it up. Do not use the oven to dry the cooktop.
The Misplaced Cap
LG burner caps sit on the burner head in one position, located by the shape of the head. A cap replaced slightly off centre after cleaning leaves the ports partly covered on one side and the gas leaving in the wrong direction, so the spark clicks beside a burner that never fills. With the range unplugged and every knob off, lift the cap off, then lower it back onto the head so it sits flat and does not rock. Do the same for the grate, which can also sit on the cap edge if it is skewed.
Blocked Ports
Boiled-over sauce and sugar bake hard into the small ports around the burner head. With the cap off and the range unplugged, clean the ports with a soft brush and a wooden toothpick or a straightened paper clip, never a metal pin that can enlarge them, then wipe and dry the head. Check that the igniter tip is clean; a film of grease across it stops the spark reaching the gas. Wipe it with a cotton swab and rubbing alcohol and let it dry.
Clicking That Will Not Stop
If every igniter on the cooktop clicks continuously with the knobs off, moisture has reached one of the spark switches behind the knobs and is holding the circuit closed. Unplug the range to silence it and let it dry for a day; if the clicking resumes when power is restored, the switch has failed and it needs replacing, which is a job behind the control panel with the range unplugged and the gas shutoff valve closed.
What Is Not an Owner Job
A burner that still will not light with a dry, clean, correctly seated head, or one that lights with a weak, yellow or lifting flame, points at the spark module, the igniter itself, the burner valve or the gas pressure regulator. All of those are reached with the range unplugged and the gas shutoff valve behind the range closed, and the range moved away from the wall without straining its flexible gas connector. That sequence is a technician's, not an evening project. Book an LG range repair and say which burner is affected, whether the igniter clicks, and whether the problem started after cleaning.