Lithium Grease 101;
Grease is nothing more than OIL held in suspension by chemical thickeners, technically called SOAPS. Think of grease as a sponge that releases oil as it is required (worked) and draws it back into suspension when it is not required (resting).
Lithium is one of many types of soap thickeners. There are also many types of Lithiums, listed here in approximate order of performance : Lithium, Lithium 12 hydroxystearate, Lithium Complex, Lithium Polymer, and Lithium Combinations to name a few.
Automotive Lithium greases are traditionally low cost greases that provide relatively good high and low temp performance, good shear strength and relatively good water resistance, hence their wide use in automotive applications.
All greases, regardless of their soap base e.g. Barium, Bentone, Sodium, Aluminium Complex, Polyurea and Calcium's increase their performance characteristics primarily by the addition of and amount of additives, plus the type base oil used in the grease formulations.
Bottom Line;
NOT all Lithiums are created equal. Why, because of the additives, base oils, viscosity, polymers, EP/AW packages etc.,etc.
Lithium info you can use on your bike;
Basically ALL Automotive GP (General Purpose) Lithium greases are acceptable for use in bike lubrication, IMHO.
However, you should avoid using "performance" type EP (Extreme Pressure) Lithium greases and certainly Industrial grade EP Lithium greases and Lithiums that are extremely tacky. Lithium, NLGI grade No.#2 greases that are smooth, tan or amber in colour and buttery in texture are quite often the best to use in bikes.
PS,
Marine grade Lithium greases typically use higher concentrations of tackifiers (sticky stuff or ParaTac) which MAY slow down your free wheeling rolling speed.
Typically, waxes are not "usually" added to Lithiums. The waxes in grease is often the result of the type of base oil used in making grease, such as Parrafinic (wax) verses Napthenic (non-wax) or de-waxed base oils.