is it necessary to use a lock washer (other than split) when applying torque to a bolt?
No, why would you think so? (edit: not beating up on you, but maybe you have good reasons for thinking so) Do you see a washer of any kind on wheel nuts? edit: Ok, maybe some do, but not generally. A lock washer can help prevent a nut from backing off under vibration loads…but not many lockwasher designs are good at really doing that - see Nordlock for an example of one that does work).
Washers can help prevent embedment of a steel nut into softer material, or provide a good flat faying surface for the nut over a rougher-machined part. But I make a lot of parts with counter-bored and spotfaced surfaces for bolts to avoid having to have washers added to the BOM.
Getting the torque right starts with a bolt joint calculation (see Shigley’s Mechanical Engineering Design or other texts for these) followed by experimentation and possibly FEA, to determine the bolt tightening specs for the shop guys. Often, a number of turns or partial turns spec. turns out to give more repeatable results than a torque wrench.
edit: good to see you here, there are quite a few people here who like answering questions.
There is a lot of literature out there that says that lock washers don’t work.
since not knowing bolt size, other options to consider are:
Thanks for your response I think lug nuts are a bad example since they’re somewhat countersunk like a flat head.