Most of the Lawn Chief equipment was made by MTD or older units may have been made by ATLAS. In any case, The most recent ones were made by NOMA which was purchased by Murray, Which as gone out of business and part of the operation was taken over by Briggs & Stratton.
The MTD or the Briggs & stratton site is the site you need to go to, but don't be surprised if they do not list anything for your unit. It is very old and most parts are NOT available. Atlas has been out of business for MANY ears. One solution might be to start checking with some of the older lawn mower shops and see if they might have an old unit you can take a handle off of. IF you don't find one that way, you may try taking the whole unit to one of these shops and see if they might have anything else that they might be able to MAKE work. We do this sort of thing at our shop all the time.
Here is a link to the MTD Site.
I have not been able to cind the model you mentioned, but you may end up contacting them by phone.
Also here is a link that shows many of the other links to obsolete snowthrowers. IT might help you in your quest.