[LH Lead-Foot]

P0157 and P0137 are codes that indicate 02 sensor in front of the catalytic converter. The engine has to be in closed loop, basically run above 1500 PRM's for 2 minutes. Low voltage = lean or way too much oxygen. I taught tech's to think of them as "Hydrocarbon Sensors" that produce higher voltage with high amounts of fuel in the exhaust. They produce voltages from 0.1 v - 1.0 v normally.

If behind the catalytic converters, their signal moves very little to indicate the cat's ability to store oxygen. Are the 02 sensor in front of the cat? If so, that is bank 1 or 2, sensor 1.

You indicated the problem follows the sensor even when replaced. This kinda removes melted wires either PPL or TAN. How are you getting these codes? Scan-tool of parts store plugging in their code reader, because what you are describing is somewhat confusing. These should be 4 wire sensors, with 2 being heaters to quickly get them into "Closed Loop".

Make sure the are putting the correct information into the scan-tool, like Year, Model and VIN 8th digit for engine 5.7L in your case.

Make sure the wire terminals are ok, tight fit, not pushed out & clean. Most schematics show only one connector between the 02 to VCM, which is the sensors connector only. So weird.

One possibility is the controller, in this case called the VCM, is not grounded well to the body, engine and back to the battery. If you have a good digital multi-meter (DMM), Lets do a voltage drop test to check the VCM.

Back probing a ground wire, like the MAP sensor. It has a vacuum hose to it, but 3 wires. One is GRY that measure 5 volts, key on, engine off. The BLK wire is dedicated ground that goes back into the VCM, out thru ground to G100, block, battery cable to battery. The LT GRN is MAP input into VCM...ignore.

Back probe the black wire without damage, using a "TEE" pin (Sold at fabric stored) to DMM, set to DC Voltage, connect other meter led to negative battery, start engine and take measurement. It should be lower than 0.400 volts (0.4). If higher like 1.23 volts, you have a problem.

VCM or PCM (Computer in general) have multiple grounds that exit the module from the Memory, Input, Output, Clock section. They are not soldered together inside the computer and go to G104, G103, which is out of harness to engine. So double check the battery ground cable and clean battery connection...also chassis or body. Grounds everywhere!

Other issues to answer;
#1 Do you have a cat?
#2 Do you have catalytic converters or have they been replaced?
#3 Are these 4 wire heated 02 sensors? (Should be)
#4 Have the sensor(s) been dropped onto hard surface?
#5 Have the sensor wires / harness been soldered?
#6 Did codes get cleared between repairs. Lean for 70 seconds, set code, but is a "Type B" code which means you have to have two (2) key cycles before it will turn on MIL.
The MIL goes off after 3 consecutive drive trips when test runs and passes. What is a "Drive Trip"? Engine coolant temp and intake air temp are within 10 degrees of each other, reaches 172 degrees or higher / also called "Warm-up Cycles".

The sensor's behind or down-stream of the cat, has only reason to be there is to guarantee the catalytic converters condition.
Hope this helps a little.