My Lexus has been gently driven with under 26000km 16000 miles but, when travelling over a modest bump at 50 km or less the left rear suspension has a hard jarring knock. Is this a shock problem.

check the springs and the shock absorber, your shock will almost certainly need replacing, servicing if you are lucky and it is the
serviceable type.

sounds like the shock absorbers need changing

sounds like a timing belt issue. Toyotas will run forever if you change the timing belt every 100,000 km, or 65,000 miles

Most likely it is a bent or seized shock absorber - remove and test by hand and replace if necessary. For best practice replace in pairs.

This is simple the air suspension air bags are leaking, they last about 75-100,00 miles on this model, even less if driven on harsh roads or off road.

2002 Lexus ls430 check VSC message

takes a long time to run the rediness test since there are 6 different tests to complete...

PROCEDURE 1
EVAPORATIVE EMISSION SYSTEM LEAK MONITOR
Inspection Conditions
Engine coolant temperature: 30°C (75°F) or less (The engine is stopped before the test drive is started).
Atmospheric temperature: 5 - 30°C (41 - 113°F).
Condition of A/T: Selector lever D range.
Fuel remained in fuel tank: 30 - 50% is recommended.
Time required: 16 minutes or less after started the engine.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position. Well be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start.
Accelerate until the vehicle speed is 89 km/h (55 mph) or more.
While keeping the accelerator pedal opening degree constant, keep the vehicle speed at 89 km/h (55 mph) or more and travel for 16 minutes.
Return the vehicle to the shop, then turn the ignition switch to "LOCK" (OFF) position.

PROCEDURE 2
FUEL TRIM MONITOR
Drive Cycle Pattern
Inspection Conditions
Engine coolant temperature: 100°C (212°F) or less.
Atmospheric temperature: -10 - 60°C (14 - 140°F).
Condition of A/T: Selector lever D range.
Time required: 30 minutes or more.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position). Will be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start.
Accelerate until the vehicle speed is 89 km/h (55 mph) or more.
While keeping the accelerator pedal opening degree constant, keep the vehicle speed at 89 km/h (55 mph) or more and travel for 30 minutes.
Return the vehicle to the shop, then turn the ignition switch to "LOCK" (OFF) position

PROCEDURE 3
CATALYTIC CONVERTER MONITOR
Drive Cycle Pattern
Inspection Conditions
Atmospheric temperature: -10°C (14°F) or more.
Condition of A/T: Selector lever D range.
Engine coolant temperature: Not set.
Time required: 16 minutes or more.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position). Will be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start.
Accelerate until the vehicle speed is 89 km/h (55 mph) or more.
Travel for 300 seconds or more while keeping the vehicle speed at 89 km/h (55 mph) or more.
Decelerate until the vehicle speed is within 80 km/h (50 mph) or less.
While traveling at 56 - 80 km/h (35 - 50 mph) for 10 minutes or more, fully close the throttle at least once in 2 minutes and decelerate for 10 seconds or more.
Do not repeat deceleration too often.
Vehicle speed may go below 56 km/h (35 mph) after the deceleration.
Stopping and braking are permitted. (If stopped or drive at 56 km/h (35 mph) or less for more than 5 minutes the monitoring may be stopped. In this case please restart monitoring from the beginning.)
After completing the above deceleration, bring the vehicle speed back to 56 - 80 km/h (35 - 50 mph) and keep it in the range until starting the deceleration again.
Repeat the above deceleration at least 5 times.
Return the vehicle to the shop, then turn the ignition switch to "LOCK" (OFF) position

PROCEDURE 4
HEATED OXYGEN SENSOR MONITOR
Drive Cycle Pattern
Inspection Conditions
Engine coolant temperature: 100°C (212°F) or more.
Atmospheric temperature: -10°C - 60°C (14 - 140°F) or more.
Condition of A/T: Selector lever D range.
Time required: 16 minutes or more.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position). Will be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start.
Accelerate until the vehicle speed is 56 - 80 km/h (35 - 50 mph).
While keeping the accelerator pedal opening degree constant, keep the vehicle speed at 56 - 80 km/h (35 - 50 mph) and travel for 16 minutes or more.
Stopping and braking during this operation are permitted. Keep the accelerator opening degree constant for 1 minute or more after each acceleration.
Return the vehicle to the shop, then turn the ignition switch to "LOCK" (OFF) position

PROCEDURE 5
EXHAUST GAS RECIRCULATION (EGR) SYSTEM MONITOR
Drive Cycle Pattern
Inspection Conditions
Engine coolant temperature: 100°C (212°F) or less.
Atmospheric temperature: 5 - 60°C (41 - 140°F).
A/C switch: OFF.
Condition of A/T: Selector lever D range.
Time required: 16 minutes or more.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position). Will be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start.
Accelerate until the vehicle speed is 56 - 80 km/h (35 - 50 mph).
While traveling 16 minutes or more at 56 - 80 km/h (35 - 50 mph) with engine speed 2,000 r/min or above, fully close the throttle at decelerate for 5 seconds or more until the engine speed reaches 1,000 r/min or under.
Do not repeat deceleration too often.
Stopping and braking are permitted (Rapid deceleration and sharp steering are not permitted).
After completing the deceleration, bring the vehicle speed back to 56 - 80 km/h (35 - 50 mph) and keep it in the range until starting the deceleration again.
Repeat the above deceleration at least 8 times by fully closing the throttle valve.
Return the vehicle to the shop, then turn the ignition switch to "LOCK" (OFF) position

PROCEDURE 6
OTHER MONITOR (Main Components, Sensors & Switches, Wire Breakage & Short Circuit)
Drive Cycle Pattern
Inspection Conditions
Engine coolant temperature:
100°C (212°F) or less (Except engine coolant temperature sensor monitoring).
30°C (86°F) or less (Engine coolant temperature sensor monitoring).
Atmospheric temperature:
5°C (41°F) or more (Except engine coolant temperature sensor monitoring).
-10°C (14°F) or less (Engine coolant temperature sensor monitoring).
Condition of A/T: Selector lever D range.
Time required: 21 minutes or more.
Drive cycle pattern: One trip monitor (from start to ignition switch to "LOCK" (OFF) position). Will be completed while traveling with the following drive cycle pattern.
Test Procedure
Engine: start
Accelerate until the vehicle speed is 56 km/h (35 mph) or more.
While keeping the accelerator pedal opening degree constant, keep the vehicle speed at 56 km/h (35 mph) or more and travel for 16 minutes or more.
Return the vehicle to the shop.
After stopping the vehicle, continue idling for 5 minutes, and then turn the ignition switch to the "LOCK" (OFF) position. Moreover, the vehicle should be set to the following conditions for idling.
A/C switch: OFF
Lights and all accessories: OFF
Transmission: Neutral

shocks do not last forever

bad suspension in the rear

THese cars have a high speed rated tire and will almost always wear quickly. The right rear is the drive wheel (where the power goes when you give it gas) It will wear real quickly if you drive it hard. I would try rotating every 7500 miles (unless tire sizes are different as with the SL series) I sell a lot of tires on these cars and 25K is usually the limit.