Here's some practical information regarding axle grease. It's something most of us don't need to use today but very important for our 19th Century characters. Below the most recent tidbit you'll find a link to a previous post on Axle Grease for Wagons.
Axle-grease for very heavy wagons. No. 1, for winter: Tallow, 420 parts; palm oil, 840; soda, 140; water, 4200.
No. 2, for summer: Tallow, 420 parts; palm oil, 490; soda, 35; water, 2300.
The above lubricants are calculated for a low temperature in winter and a hot one in summer. For a moderate winter climate, the quantity of soda may be somewhat reduced, and that of palm oil increased.
Axle grease for heavy wagons. Palm oil, 210 parts; tallow, 85; soda lye, 65; water, 920.
Melt the palm oil and tallow together, and after making the mixture homogeneous by stirring, add the soda lye. The latter is prepared by dissolving soda in sufficient hot water for the cooled fluid to show 20° or 21° Be. After adding and stirring in the soda lye, the water is added, and the whole stirred to a homogeneous mass, which is ladled into vessels and allowed to congeal.
Grease for wooden machinery. Tallow, 30 parts; palm oil, 20; train oil, 10; graphite, 20.
After melting the fats at a moderate heat, intimately mix the graphite, previously pulverized and elutriated, with the mass by stirring.
Source: A Practical Treatise on animal and vegetable fats and oils ©1896
Here's the link to the previous post. Axle Grease For Your Wagon or Carriage