My kenmore 80 series washer at the end of the spin cycle or when the lid is lifted it will lurch from side to side.

This assumes that you have a KENMORE top load, direct drive, neutral drain washers are made Whirlpool.

First, see the Sears parts site for your washer:
http://www.searspartsdirect.com/partsdirect/index.action

Enter your model number (###.######) and you'll see a list of major sub-components with diagrams and parts.

The problem points to the brake.

The washer uses a brake system to stop the basket at the end of the spin cycle OR when the lid is raised during the spin.

Just like a brake on a car, it's designed to slip a bit so that the basket / car doesn't come to an abrupt halt.

Over time, the brake shoes can jam against the brake drum and bring the basket to a halt too quickly with a lot of noise.

A way to solve this (that I tried and it works) is to pull the basket tube / brake assembly and if the brake shoes look OK, spray a small amount of silicone spray on the inside of the brake drum.

Following is a description of how to remove the cabinet, pump, motor, transmission and basket drive tube on Whirlpool / Kenmore / Roper direct drive washers.

As an aside, you don't need a special spanner wrench to remove the spanner nut. I've found that a short (10") pipe wrench hooked over one of the spanner nut tabs and tapped with a hammer will usually loosen the nut. Also, rather than hitting the Drive block directly with a hammer, put a short piece of wood under it first to protect it.

http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=16&newsdesk_id=137


Following are the Whirlpool Service manual for this type of washer and the Whirlpool parts list for their commercial washers although the consumer models are basically the same.

https://secured.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/f7e2147fa98b28cf85257122007475cb/$FILE/L-55.pdf

http://shared.whirlpoolcorp.com/assets/pdfs/literature/Repair%20Part%20List%20-%20W10114743.pdf