This is a pain-in-the-butt job lubricating the lower assembly units especially. Ideally, the whole lots dismantled to apply the grease. I just bought one of these.
www.ebay.com.au/itm/164194095042?_trkparms=amclksrc%3DITM%26aid%3D1110013%26algo%3DHOMESPLICE.SIMRXI%26ao%3D1%26asc%3D259212%26meid%3Da68e0124fae04d9cb9861addbaf4be5f%26pid%3D101196%26rk%3D2%26rkt%3D12%26sd%3D326009128881%26itm%3D164194095042%26pmt%3D1%26noa%3D0%26pg%3D4429486%26algv%3DSimRXIVINativeV1WithMMV3&_trksid=p4429486.c101196.m2219&itmprp=cksum%3A164194095042a68e0124fae04d9cb9861addbaf4be5f%7Cenc%3AAQAJAAABEPgtYNYr074Rbd625X3At8xEaDSiuIYQDLYzU38yXPLm9KV1H7KhOlqhnQrMEYYF2jCcfCETel0dSSuEeYFoDNmdMXe%252B6wYB7Y1eMdx0TgTIEan%252B2bKjHN1sNH6q5xqSx4pBlLp%252BFTMPe3RtlGmPz1Ow96nyn7a%252F8gOG3%252FWjxwmJ%252FhAEW%252FmLS0lZFYoq4xj8nCvo%252FmmTR39FpnramiMckYvZjgKIqDxSDc3zC%252F6c0EtzXdfQHGNdkZdPNcFhHXIO0F3mnxoTn6hOz8DfN9UBeCknb5RjNYxq052oo0SPGHzMGdvfdRoRCBjsiQtgQLUchMvfooFS34c5FfvnSgKoE1XDwDJ7Xcq%252FJqXfmdAMZBC0%7Campid%3APL_CLK%7Cclp%3A4429486&itmmeta=01J2W942E4PM4NTPTW69NWSZX5
Meant for bicycles but looks ideal for the job. The grease is waterproof or you have a choice of other greases that come in the tubes with toothpaste threads.
www.ebay.com.au/itm/326009128881?itmmeta=01J2W937E1Z4HE52G4RXRPCCH9&hash=item4be7a887b1:g:V5YAAOSwQkxlzAyU&itmprp=enc%3AAQAJAAAA8D0riSx84lR9zqXgqhAYIsj8OSremAyt8iBLcRLG9K63T47okCzhP8liwooaokm%2FBStZ6iprnT9rWBfRyJJf48HP3x774fzVYV6%2B3IxwiN2XPdltuYEW05ekiyjKJHClZo7ul0fHhV0pkfEnFT3y3XU0VxRUvpq%2B9kXpEgXYK6GlQzaQ5gzsFXtMrZjz%2BadeZtc%2BH0gdm%2FPzvW7PaMkA1ueNIufxDf6%2F8wE74D3qHVIMqUXE3B7EZUume30KW%2B2%2BUUN6LnjDG%2FIPhHnU7x%2BbiVRtE8POPGxWAoxrmOZ66TnMv3AK5Slhz%2B4TDh4M9Uq31A%3D%3D%7Ctkp%3ABk9SR4z3jImXZA