1. Find the manifest of the version you wish to download:

• v35: 5364478558014269262 (banned in all categories)
• v36: 9203317006213417163 (banned in all categories)
• v37: 1400894170520793128 (banned in all categories)
• v38: 5827253028426135854 (banned in all categories)
• v40: 8596342981027780916
• v45 Before Hotfixes: 7793868886336446019 (selling items acquired from giftboxes is banned)
• Final v45: 7637156099460715726
• v47: 8928166772742545463
• v48: 6898658145923649977
• v49: 7525563530173177311
• v50: 1283771170253079985
• v50 hotfix: 2961956797830002840
• v56: 6074226372806880905
• v56 hotfix: 6648293528411358330
• v60: 2052574930329540389 (days that spawn 0 interior items are banned in the 100% categories)
• v61: 7915974652113524458
• v62: 6781127831766068218
• v62 hotfix: 2681997312468718444
• v64: 8158077314512521071
• v64 hotfix: 1436342303485508317
• v65: 45218974618910766
• v65 hotfix: 4399152805243356613
• v66: 4738384637822614526
• v67: 5016628524348387397
• v68: 4025643880645587046
• v69: 8926104470782461485
• v69 Hotfix: 1111763047378210033
• v69 New years patch: 1367019593609280205

(Thanks to @OkiaBetter for finding the manifests for v40 and v45, @Tomatobird8 for v50's and v56's, @Escue for finding v60, 61, 62, 64, 65.2 and 66 and @1A3Dev for the rest.)

2. Press windows key and r.
3. Enter steam://open/console into the prompt that comes up.
4. Enter the command: download_depot 1966720 1966721 <manifestID>. Enter the manifest of the version you wish to download into <manifestID>. For example, if you wanted to downpatch to v40, you would enter the command: download_depot 1966720 1966721 8596342981027780916
5. Wait for it to download. This may take a while. Once it is downloaded, it will give you a prompt saying, "Depot download complete" with a line showing you which file directory it downloaded under.
6. To find the files, navigate to your Steam folder and go to Steam > steamapps > content > app_1966720 > depot_1966721 If you wish to download multiple versions, make sure to move the Lethal Company files out of the folder otherwise the next download will overwrite the previous download.

For a visual tutorial on how to do this, please see: