Thank you for your question and I understand your concern.
To begin with, this top loading Kenmore washer does not have a lid lock. It has a lid switch and if the lid switch is broken or faulty, the washer will not operate in any of the drain and spin cycles. Based on your symptom and details, the lid switch is likely broken or faulty.
The lid switch is fastened with a couple of screws and it is located under the top. In order to access and replace the lid switch, the cabinet must be taken off the base.
To remove the washer cabinet:
Disconnect the power cord from the power source.
Remove the screw located at the bottom of the control panel end caps.
Slide the control panel towards the front of the washer and lift it up and hinge it over the rear panel.
Disconnect the three wire lid switch harness connector from the top of the washer.
Use a flat blade screwdriver to release the two gold colored cabinet clips securing the top of the cabinet to the back panel. Place the tip of the screwdriver in the first valley and then push the screwdriver handle back towards the rear panel.
Open the lid and grasp the opening and tilt the top of the cabinet towards you at 20 degree angle and walk the cabinet out so you can access the lid switch. Remove the two screws on the side of the opening to remove the lid switch.
I added an image below showing how to remove the cabinet. If the image is too small, I added a second response with a image that will open larger.
lid switch #285671 for model 110.92578210
can be ordered from Sears Parts Direct.
This may be the issue. If not, please reply and I will be glad to assist you further.